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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

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #81 : High School: Geometry

What is the supplement of the complement of $18^{\circ}$ $\displaystyle 18^{\circ}$?

Possible Answers:

$108^{\circ}$ $\displaystyle 108^{\circ}$

$72^{\circ}$ $\displaystyle 72^{\circ}$

$36^{\circ}$ $\displaystyle 36^{\circ}$

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

$18^{\circ}$ $\displaystyle 18^{\circ}$

Correct answer:

$108^{\circ}$ $\displaystyle 108^{\circ}$

Explanation:

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

We need to first find the complement of $18^{\circ}$ $\displaystyle 18^{\circ}$

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $18^{\circ}$ $\displaystyle 18^{\circ}$ we can substitute it for $\uptext{x}$ $\displaystyle \uptext{x}$, and solve for $\uptext{y}$ $\displaystyle \uptext{y}$.

$\\90 = y + 18 \\y = 72$ $\displaystyle \\90 = y + 18 \\y = 72$

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 $\displaystyle x$.

$\\180 = y + 72 \\y = 108$ $\displaystyle \\180 = y + 72 \\y = 108$

So the answer is $108^{\circ}$ $\displaystyle 108^{\circ}$.

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Example Question #82 : High School: Geometry

What is the supplement of the complement of $62^{\circ}$ $\displaystyle 62^{\circ}$?

Possible Answers:

$28^{\circ}$ $\displaystyle 28^{\circ}$

$124^{\circ}$ $\displaystyle 124^{\circ}$

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

$118^{\circ}$ $\displaystyle 118^{\circ}$

$62^{\circ}$ $\displaystyle 62^{\circ}$

Correct answer:

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

Explanation:

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

We need to first find the complement of $62^{\circ}$ $\displaystyle 62^{\circ}$

The complement is

$\displaystyle 90 = x + y$

Since we are given an angle of $62^{\circ}$ $\displaystyle 62^{\circ}$ we can substitute it for $\displaystyle x$, and solve for $\displaystyle y$.

$\\90 = y + 62 \\y = 28$ $\displaystyle \\90 = y + 62 \\y = 28$

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 $\displaystyle x$.

$\\180 = y + 28 \\y = 152$ $\displaystyle \\180 = y + 28 \\y = 152$

So the answer is $152^{\circ}$ $\displaystyle 152^{\circ}$.

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

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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 #81 : High School: Geometry

Example Question #82 : High School: Geometry

All Common Core: High School - Geometry Resources

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