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# EXAMPLE 3 PowerPoint PPT Presentation

Find m ∠ JKM. STEP 1. Write and solve an equation to find the value of x. (2 x – 5) ° =. 70 ° + x °. x =. 75. STEP 2. Substitute 75 for x in 2 x – 5 to find m ∠ JKM. 2 x – 5 =. 75. – 5 =. 2. 145. ANSWER. The measure of ∠ JKM is 145 °. EXAMPLE 3.

EXAMPLE 3

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Findm∠ JKM.

STEP1

Write and solve an equation to find the value of x.

(2x – 5)° =

70°+ x°

x =

75

STEP2

Substitute 75 for xin 2x–5 to find m∠ JKM.

2x–5 =

75

–5 =

2

145

The measure of∠ JKMis145°.

EXAMPLE 3

Find an angle measure

SOLUTION

Apply the Exterior Angle Theorem.

Solve for x.

ARCHITECTURE

The tiled staircase shown forms a right triangle. The measure of one acute angle in the triangle is twice the measure of the other. Find the measure of each acute angle.

EXAMPLE 4

Find angle measures from a verbal description

SOLUTION

First, sketch a diagram of the situation. Let the measure of the smaller acute angle be x°. Then the measure of the larger acute angle is 2x°. The Corollary to the Triangle Sum Theorem states that the acute angles of a right triangle are complementary.

x° + 2x° =

90°

x =

30

So, the measures of the acute angles are 30°and 2(30°)

=60°.

EXAMPLE 4

Find angle measures from a verbal description

Use the corollary to set up and solve an equation.

Corollary to the Triangle Sum Theorem

Solve forx.

Find the measure of 1 in the diagram shown.

The measure of∠ 1in the diagram is 65°.

for Examples 3 and 4

GUIDED PRACTICE

Find the measure of each interior angle of ABC, where mA=x , mB=2x°, and mC=3x°.

°

x

180°

A + B + C =

x + 2x + 3x =

180°

6x =

180°

2x

3x

x =

30°

2x =

2(30) =

60°

B =

3(30) =

90°

C =

3x =

for Examples 3 and 4

GUIDED PRACTICE

SOLUTION

Find the measures of the acute angles of the right triangle in the diagram shown.

26° and 64°

for Examples 3 and 4

GUIDED PRACTICE

In Example 4, what is the measure of the obtuse angle formed between the staircase and a segment extending from the horizontal leg?

A

2x

x

Q

B

C