9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem

Complementary and supplementary pairs, the 180-degree angle sum and similar-triangle proportions, and finding a missing right-triangle side with square roots.

Prealgebra 2e, 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem

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28 exercises

9.3 Exercise 1

Before you get started, take this readiness quiz.

Solve: $x + 3 + 6 = 11 .$
If you missed this problem, review the reference.

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9.3 Exercise 2

Solve: $\frac{a}{45} = \frac{4}{3} .$
If you missed this problem, review the reference.

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9.3 Exercise 3

Simplify: $\sqrt{36 + 64} .$
If you missed this problem, review the reference.

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9.3 Exercise 5

An angle measures $\text{25}° .$ Find its: ⓐ supplement ⓑ complement.

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9.3 Exercise 6

An angle measures $\text{77}° .$ Find its: ⓐ supplement ⓑ complement.

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9.3 Exercise 8

Two angles are supplementary. The larger angle is $\text{100}°$ more than the smaller angle. Find the measures of both angles.

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9.3 Exercise 9

Two angles are complementary. The larger angle is $\text{40}°$ more than the smaller angle. Find the measures of both angles.

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9.3 Exercise 11

The measures of two angles of a triangle are $\text{31}°$ and $\text{128}° .$ Find the measure of the third angle.

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9.3 Exercise 12

A triangle has angles of $\text{49}°$ and $\text{75}° .$ Find the measure of the third angle.

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9.3 Exercise 14

One angle of a right triangle measures $\text{56}° .$ What is the measure of the other angle?

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9.3 Exercise 15

One angle of a right triangle measures $\text{45}° .$ What is the measure of the other angle?

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9.3 Exercise 17

The measure of one angle of a right triangle is $\text{50}°$ more than the measure of the smallest angle. Find the measures of all three angles.

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9.3 Exercise 18

The measure of one angle of a right triangle is $\text{30}°$ more than the measure of the smallest angle. Find the measures of all three angles.

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9.3 Exercise 31

Find ⓐ the supplement and ⓑ the complement of the given angle.

$\text{53}°$

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9.3 Exercise 33

Find ⓐ the supplement and ⓑ the complement of the given angle.

$\text{29}°$

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9.3 Exercise 35

Use the properties of angles to solve.

Find the supplement of a $\text{135}°$ angle.

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9.3 Exercise 37

Use the properties of angles to solve.

Find the complement of a $27.5°$ angle.

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9.3 Exercise 39

Use the properties of angles to solve.

Two angles are supplementary. The larger angle is $\text{56}°$ more than the smaller angle. Find the measures of both angles.

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9.3 Exercise 41

Use the properties of angles to solve.

Two angles are complementary. The smaller angle is $\text{34}°$ less than the larger angle. Find the measures of both angles.

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