EXAMPLE 3 Find an angle measure SOLUTION STEP 1 Write and solve an equation to find the value of x. Apply the Exterior Angle Theorem. (2x – 5) ° = 70 °

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

EXAMPLE 4 Find angle measures from a verbal description 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. 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.

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 x ° + 2x ° = 90 ° Solve for x. x = 30 So, the measures of the acute angles are 30 ° and 2(30 ° ) = 60 °. ANSWER

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

GUIDED PRACTICE for Examples 3 and 4 SOLUTION A + B + C = 180 ° x + 2x + 3x =180 ° 6x =180 ° x =30 ° B = 2x = 2(30) =60 ° C =3x = 3(30) =90 ° x 2x2x 3x3x 4. Find the measure of each interior angle of ABC, where m A = x, m B = 2x °, and m C = 3x °. °

GUIDED PRACTICE for Examples 3 and 4 5. Find the measures of the acute angles of the right triangle in the diagram shown. 26 ° and 64 ° ANSWER

GUIDED PRACTICE for Examples 3 and 4 6. In Example 4, what is the measure of the obtuse angle formed between the staircase and a segment extending from the horizontal leg? A B C Q 2x2x x ACD =150°. ANSWER