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Common Core: High School - Geometry : Prove Line and Angle Theorems: CCSS.Math.Content.HSG-CO.C.9

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

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Example Questions

Example Question #1 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $50^{\circ}$ $\displaystyle 50^{\circ}$?

Possible Answers:

$50^{\circ}$ $\displaystyle 50^{\circ}$

$40^{\circ}$ $\displaystyle 40^{\circ}$

$130^{\circ}$ $\displaystyle 130^{\circ}$

$100^{\circ}$ $\displaystyle 100^{\circ}$

$140^{\circ}$ $\displaystyle 140^{\circ}$

Correct answer:

$140^{\circ}$ $\displaystyle 140^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $50^{\circ}$ $\displaystyle 50^{\circ}$.

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $50^{\circ}$ $\displaystyle 50^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 50 \\y = 40$ $\displaystyle \\90 = y + 50 \\y = 40$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\uptext{x}$ $\displaystyle \uptext{x}$.

$\\180 = y + 40 \\y = 140$ $\displaystyle \\180 = y + 40 \\y = 140$

So the answer is $140^{\circ}$ $\displaystyle 140^{\circ}$.

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Example Question #73 : Congruence

What is the supplement of the complement of $81^{\circ}$ $\displaystyle 81^{\circ}$?

Possible Answers:

$9^{\circ}$ $\displaystyle 9^{\circ}$

$162^{\circ}$ $\displaystyle 162^{\circ}$

$99^{\circ}$ $\displaystyle 99^{\circ}$

$171^{\circ}$ $\displaystyle 171^{\circ}$

$81^{\circ}$ $\displaystyle 81^{\circ}$

Correct answer:

$171^{\circ}$ $\displaystyle 171^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $81^{\circ}$ $\displaystyle 81^{\circ}$

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $81^{\circ}$ $\displaystyle 81^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 81 \\y = 9$ $\displaystyle \\90 = y + 81 \\y = 9$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\displaystyle x$.

$\\180 = y + 9 \\y = 171$ $\displaystyle \\180 = y + 9 \\y = 171$

So the answer is $171^{\circ}$ $\displaystyle 171^{\circ}$.

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Example Question #2 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $40^{\circ}$ $\displaystyle 40^{\circ}$?

Possible Answers:

$130^{\circ}$ $\displaystyle 130^{\circ}$

$40^{\circ}$ $\displaystyle 40^{\circ}$

$80^{\circ}$ $\displaystyle 80^{\circ}$

$50^{\circ}$ $\displaystyle 50^{\circ}$

$140^{\circ}$ $\displaystyle 140^{\circ}$

Correct answer:

$130^{\circ}$ $\displaystyle 130^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $40^{\circ}$ $\displaystyle 40^{\circ}$.

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $40^{\circ}$ $\displaystyle 40^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 40 \\y = 50$ $\displaystyle \\90 = y + 40 \\y = 50$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\displaystyle x$.

$\\180 = y + 50 \\y = 130$ $\displaystyle \\180 = y + 50 \\y = 130$

So the answer is $130^{\circ}$ $\displaystyle 130^{\circ}$

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Example Question #4 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $66^{\circ}$ $\displaystyle 66^{\circ}$?

Possible Answers:

$132^{\circ}$ $\displaystyle 132^{\circ}$

$24^{\circ}$ $\displaystyle 24^{\circ}$

$66^{\circ}$ $\displaystyle 66^{\circ}$

$114^{\circ}$ $\displaystyle 114^{\circ}$

$156^{\circ}$ $\displaystyle 156^{\circ}$

Correct answer:

$156^{\circ}$ $\displaystyle 156^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $66^{\circ}$ $\displaystyle 66^{\circ}$.

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $66^{\circ}$ $\displaystyle 66^{\circ}$ we can substitute it for $\uptext{x}$ $\displaystyle \uptext{x}$, and solve for $\uptext{y}$ $\displaystyle \uptext{y}$.

$\\90 = y + 66 \\y = 24$ $\displaystyle \\90 = y + 66 \\y = 24$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\displaystyle x$.

$\\180 = y + 24 \\y = 156$ $\displaystyle \\180 = y + 24 \\y = 156$

So the answer is $156^{\circ}$ $\displaystyle 156^{\circ}$

Report an Error

Example Question #2 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $71^{\circ}$ $\displaystyle 71^{\circ}$?

Possible Answers:

$161^{\circ}$ $\displaystyle 161^{\circ}$

$71^{\circ}$ $\displaystyle 71^{\circ}$

$109^{\circ}$ $\displaystyle 109^{\circ}$

$19^{\circ}$ $\displaystyle 19^{\circ}$

$142^{\circ}$ $\displaystyle 142^{\circ}$

Correct answer:

$161^{\circ}$ $\displaystyle 161^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $71^{\circ}$ $\displaystyle 71^{\circ}$

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $71^{\circ}$ $\displaystyle 71^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 71 \\y = 19$ $\displaystyle \\90 = y + 71 \\y = 19$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\displaystyle x$.

$\\180 = y + 19 \\y = 161$ $\displaystyle \\180 = y + 19 \\y = 161$

So the answer is $161^{\circ}$ $\displaystyle 161^{\circ}$

Report an Error

Example Question #5 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $65^{\circ}$ $\displaystyle 65^{\circ}$?

Possible Answers:

$65^{\circ}$ $\displaystyle 65^{\circ}$

$115^{\circ}$ $\displaystyle 115^{\circ}$

$155^{\circ}$ $\displaystyle 155^{\circ}$

$130^{\circ}$ $\displaystyle 130^{\circ}$

$25^{\circ}$ $\displaystyle 25^{\circ}$

Correct answer:

$155^{\circ}$ $\displaystyle 155^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $65^{\circ}$ $\displaystyle 65^{\circ}$

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $65^{\circ}$ $\displaystyle 65^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 65 \\y = 25$ $\displaystyle \\90 = y + 65 \\y = 25$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\displaystyle x$

$\\180 = y + 25 \\y = 155$ $\displaystyle \\180 = y + 25 \\y = 155$

So the answer is $155^{\circ}$ $\displaystyle 155^{\circ}$

Report an Error

Example Question #6 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $45^{\circ}$ $\displaystyle 45^{\circ}$?

Possible Answers:

$135^{\circ}$ $\displaystyle 135^{\circ}$

$90^{\circ}$ $\displaystyle 90^{\circ}$

$45^{\circ}$ $\displaystyle 45^{\circ}$

$135^{\circ}$ $\displaystyle 135^{\circ}$

Correct answer:

$135^{\circ}$ $\displaystyle 135^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $45^{\circ}$ $\displaystyle 45^{\circ}$

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $45^{\circ}$ $\displaystyle 45^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 45 \\y = 45$ $\displaystyle \\90 = y + 45 \\y = 45$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\displaystyle x$

$\\180 = y + 45 \\y = 135$ $\displaystyle \\180 = y + 45 \\y = 135$

So the answer is $135^{\circ}$ $\displaystyle 135^{\circ}$.

Report an Error

Example Question #7 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $76^{\circ}$ $\displaystyle 76^{\circ}$?

Possible Answers:

$76^{\circ}$ $\displaystyle 76^{\circ}$

$152^{\circ}$ $\displaystyle 152^{\circ}$

$14^{\circ}$ $\displaystyle 14^{\circ}$

$166^{\circ}$ $\displaystyle 166^{\circ}$

$104^{\circ}$ $\displaystyle 104^{\circ}$

Correct answer:

$166^{\circ}$ $\displaystyle 166^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $76^{\circ}$ $\displaystyle 76^{\circ}$

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $76^{\circ}$ $\displaystyle 76^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 76 \\y = 14$ $\displaystyle \\90 = y + 76 \\y = 14$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\displaystyle x$.

$\\180 = y + 14 \\y = 166$ $\displaystyle \\180 = y + 14 \\y = 166$

So the answer is $166^{\circ}$ $\displaystyle 166^{\circ}$.

Report an Error

Example Question #8 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $48^{\circ}$ $\displaystyle 48^{\circ}$?

Possible Answers:

$96^{\circ}$ $\displaystyle 96^{\circ}$

$132^{\circ}$ $\displaystyle 132^{\circ}$

$138^{\circ}$ $\displaystyle 138^{\circ}$

$48^{\circ}$ $\displaystyle 48^{\circ}$

$42^{\circ}$ $\displaystyle 42^{\circ}$

Correct answer:

$138^{\circ}$ $\displaystyle 138^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $48^{\circ}$ $\displaystyle 48^{\circ}$.

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $48^{\circ}$ $\displaystyle 48^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 48 \\y = 42$ $\displaystyle \\90 = y + 48 \\y = 42$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\displaystyle x$.

$\\180 = y + 42 \\y = 138$ $\displaystyle \\180 = y + 42 \\y = 138$

So the answer is $138^{\circ}$ $\displaystyle 138^{\circ}$

Report an Error

Example Question #9 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

What is the supplement of the complement of $4^{\circ}$ $\displaystyle 4^{\circ}$?

Possible Answers:

$4^{\circ}$ $\displaystyle 4^{\circ}$

$8^{\circ}$ $\displaystyle 8^{\circ}$

$176^{\circ}$ $\displaystyle 176^{\circ}$

$94^{\circ}$ $\displaystyle 94^{\circ}$

$86^{\circ}$ $\displaystyle 86^{\circ}$

Correct answer:

$94^{\circ}$ $\displaystyle 94^{\circ}$

Explanation:

In order to solve this problem, we need to break down each word.

We need to first find the complement of $4^{\circ}$ $\displaystyle 4^{\circ}$

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $4^{\circ}$ $\displaystyle 4^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 4 \\y = 86$ $\displaystyle \\90 = y + 4 \\y = 86$

Now since we need to find the supplement of the answer, we just got.

The supplement is

$\displaystyle 180 = x + y$

Now we simply substitute the answer we just got for $\displaystyle x$.

$\\180 = y + 86 \\y = 94$ $\displaystyle \\180 = y + 86 \\y = 94$

So the answer is $94^{\circ}$ $\displaystyle 94^{\circ}$

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Common Core: High School - Geometry : Prove Line and Angle Theorems: CCSS.Math.Content.HSG-CO.C.9

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #1 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #73 : Congruence

Example Question #2 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #4 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #2 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #5 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #6 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #7 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #8 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

Example Question #9 : Prove Line And Angle Theorems: Ccss.Math.Content.Hsg Co.C.9

All Common Core: High School - Geometry Resources

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