EXAMPLE 3 Find an angle measure Find m

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

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

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

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

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

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 2 x B ANSWER ACD =150°. x C Q