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EXAMPLE 3

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.

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EXAMPLE 3

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  1. 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 ANSWER The measure of∠ JKMis145°. EXAMPLE 3 Find an angle measure SOLUTION Apply the Exterior Angle Theorem. Solve for x.

  2. 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.

  3. x° + 2x° = 90° x = 30 So, the measures of the acute angles are 30°and 2(30°) ANSWER =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.

  4. Find the measure of 1 in the diagram shown. The measure of∠ 1in the diagram is 65°. ANSWER for Examples 3 and 4 GUIDED PRACTICE

  5. 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

  6. Find the measures of the acute angles of the right triangle in the diagram shown. ANSWER 26° and 64° for Examples 3 and 4 GUIDED PRACTICE

  7. 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 ANSWER ACD =150°. for Examples 3 and 4 GUIDED PRACTICE

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