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Common Core: 7th Grade Math : Solve Simple Equations for an Unknown Angle in a Figure: CCSS.Math.Content.7.G.B.5

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Example Questions

Example Question #1 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

One angle of an isosceles triangle has measure $110^{\circ }$ . What are the measures of the other two angles?

Possible Answers:

Not enough information is given to answer this question.

$45^{\circ }, 45^{\circ }$

$35^{\circ },35^{\circ }$

$110 ^{\circ }, 40 ^{\circ }$

$70^{\circ }, 70^{\circ }$

Correct answer:

$35^{\circ },35^{\circ }$

Explanation:

An isosceles triangle not only has two sides of equal measure, it has two angles of equal measure. This means one of two things, which we examine separately:

Case 1: It has another $110^{\circ }$ angle. This is impossible, since a triangle cannot have two obtuse angles.

Case 2: Its other two angles are the ones that are of equal measure. If we let be their common measure, then, since the sum of the measures of a triangle is $180^{\circ }$ ,

x + x + 110 = 180

2x + 110 = 180

2x + 110 -110= 180 -110

2x= 70

$2x \div 2= 70 \div 2$

x = 35

Both angles measure $35^{\circ}$

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Example Question #2 : How To Find The Measure Of An Angle

Two angles are supplementary and have a ratio of 1:4. What is the size of the smaller angle?

Possible Answers:

$144^{\circ}$

$45^{\circ}$

$36^{\circ}$

$18^{\circ}$

$72^{\circ}$

Correct answer:

$36^{\circ}$

Explanation:

Since the angles are supplementary, their sum is 180 degrees. Because they are in a ratio of 1:4, the following expression could be written:

$x+4x=180$

$5x=180$

$x=36^{\circ}$

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Example Question #6 : How To Find The Measure Of An Angle

What angle is complementary to $65$^{\circ}$$ ?

Possible Answers:

$130$^{\circ}$$

$25$^{\circ}$$

$115$^{\circ}$$

$65$^{\circ}$$

$35$^{\circ}$$

Correct answer:

$25$^{\circ}$$

Explanation:

To find the other angle, subtract the given angle from $90$^{\circ}$$ since complementary angles add up to $90$^{\circ}$$ .

The complementary is:

$\angle 90-\angle65 = \angle25$

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Example Question #11 : How To Find The Measure Of An Angle

What is the supplementary angle to $100$^{\circ}$$ ?

Possible Answers:

$170$^{\circ}$$

$10$^{\circ}$$

$280$^{\circ}$$

$70$^{\circ}$$

$80$^{\circ}$$

Correct answer:

$80$^{\circ}$$

Explanation:

Supplementary angles add up to $180$^{\circ}$$ . In order to find the correct angle, take the known angle and subtract that from $180$^{\circ}$$ .

$180$^{\circ}$ -100$^{\circ}$ = 80$^{\circ}$$

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Example Question #1 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

What angle is complement to $\frac{\pi}{6}$ ?

Possible Answers:

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{2\pi}{3}$

$\frac{\pi}{6}$

$\frac{\pi}{9}$

Correct answer:

$\frac{\pi}{3}$

Explanation:

The complement to an angle is ninety degrees subtract the angle since two angles must add up to 90. In this case, since we are given the angle in radians, we are subtracting from $\frac{\pi}{2}$ instead to find the complement. The conversion between radians and degrees is: $\pi \textup{ radians } = 180 \textup{ degrees}$

$\frac{\pi}{2}-\frac{\pi}{6}$

Reconvert the fractions to the least common denominator.

$\frac{\pi}{2}-\frac{\pi}{6} = \frac{3\pi}{6}-\frac{\pi}{6} = \frac{2\pi}{6}$

Reduce the fraction.

$\frac{2\pi}{6} = \frac{\pi}{3}$

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Example Question #91 : Plane Geometry

Exterior_angle

Note: Figure NOT drawn to scale.

What is the measure of angle

Possible Answers:

y = 124

y = 134

y = 152

y = 129

y = 142

Correct answer:

y = 124

Explanation:

The two angles at bottom are marked as congruent. One forms a linear pair with a $152 ^{\circ }$ angle, so it is supplementary to that angle, making its measure $(180-152)^{\circ } = 28^{\circ }$ . Therefore, each marked angle measures $28^{\circ }$ .

The sum of the measures of the interior angles of a triangle is $180^{\circ }$ , so:

y + 28 + 28 = 180

y +56= 180

y +56-56 = 180-56

y = 124

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Example Question #3 : Triangles

One of the base angles of an isosceles triangle is $42^{\circ}$ . Give the measure of the vertex angle.

Possible Answers:

$86 ^{\circ}$

$98 ^{\circ}$

$96 ^{\circ}$

$100^{\circ}$

$90^{\circ}$

Correct answer:

$96 ^{\circ}$

Explanation:

The base angles of an isosceles triangle are always equal. Therefore both base angles are $42^{\circ}$ .

Let the measure of the third angle. Since the sum of the angles of a triangle is $180^{\circ}$ , we can solve accordingly:

$42+42+x=180\Rightarrow x=180-84\Rightarrow x=96^{\circ}$

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Example Question #2 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

The figure represents a set of complementary angles, solve for .

Possible Answers:

$52^\circ$

$53^\circ$

$55^\circ$

$56^\circ$

$54^\circ$

Correct answer:

$56^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+34=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+34=90\\ -34-34\end{array}}{x= 56}$

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Example Question #3 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

The figure represents a set of complementary angles, solve for .

Possible Answers:

$67^\circ$

$64^\circ$

$68^\circ$

$66^\circ$

$65^\circ$

Correct answer:

$65^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+25=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+25=90\\ -25-25\end{array}}{x= 65}$

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Example Question #4 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

The figure represents a set of complementary angles, solve for .

Possible Answers:

$69^\circ$

$68^\circ$

$70^\circ$

$71^\circ$

$67^\circ$

Correct answer:

$70^\circ$

Explanation:

Complementary angles are defined as two angles that when added together equal $90^\circ$

From the question, we know that the two angles are complimentary, and thus equal $90^\circ$ , so we can set up the following equation:

x+20=90

Next we can solve for :

$\frac{\begin{array}[b]{r}x+20=90\\ -20-20\end{array}}{x= 70}$

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Common Core: 7th Grade Math : Solve Simple Equations for an Unknown Angle in a Figure: CCSS.Math.Content.7.G.B.5

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #1 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Example Question #2 : How To Find The Measure Of An Angle

Example Question #6 : How To Find The Measure Of An Angle

Example Question #11 : How To Find The Measure Of An Angle

Example Question #1 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Example Question #91 : Plane Geometry

Example Question #3 : Triangles

Example Question #2 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Example Question #3 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

Example Question #4 : Solve Simple Equations For An Unknown Angle In A Figure: Ccss.Math.Content.7.G.B.5

All Common Core: 7th Grade Math Resources

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