Section 9.3 Part 1: Solve Problems with Angle Measures and Similar Triangles

One angle of a right triangle measures 69∘. What is the measure of the third angle?

21 deg

The difference of a number and five is negative one. Find the number.

4

The measures of two angles of a triangle are 66∘ and 72∘. Find the measure of the third angle.

42 Step 1. Read the problem. Draw the figure, and label it with the given information. Step 2. Identify what you are looking for. the measure of the third angle in a triangle Step 3. Name. Choose a variable to represent it. Let x= the measure of the angle. Step 4. Translate. Write the appropriate formula, and substitute. m∠A+m∠B+m∠C=180 Step 5. Solve the equation. 66+72+x=180 138+x=180 x=42 Step 6. Check. 66+72+42=180 180✓ Step 7. Answer the question. The measure of the third angle is 42 degrees.

One angle of a right triangle measures 42∘. What is the measure of the third angle?

48

Two angles are complementary. The larger angle is 12∘ more than the smaller angle. Find the measure of the larger angle.

51

The measures of two angles of a triangle are 71∘ and 58∘. Find the measure of the third angle.

51 71+58+x=180 x=51

Two angles are complementary. The larger angle is 40∘ more than the smaller angle. Find the measure of the larger angle.

65

The sum of three times a number and ten is thirty-four. Find the number.

8

ΔABC and ΔXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of each triangle.

a=7.8 y=4

Solve: m/22=−10/11.

m=-20

An angle measures 49∘. Find a.its supplement and b.its complement.

supp 131 comp 41

An angle measures 32∘. Find a. its supplement and b. its complement.

supp 148 comp 58

Two angles are supplementary. The larger angle is 100∘ more than the smaller angle. Find the measure of the larger angle.

supp 150 comp 60

An angle measures 25∘. Find its ⓐ supplement and ⓑ complement.

supp 155 comp 65

Solve: −7/y=−7/24.

y=24

An angle measures 26∘. Find a. its supplement and b. its complement.

ANSWER supplement 116 deg and complement 64 deg a.Write the appropriate formula for the situation, and substitute in the given information. m∠A+m∠B=180 26+B=180 Solve the equation. B=154 Check. 26+154=180 =180 The supplement of the 26∘ angle is 154∘. b.Write the appropriate formula for the situation, and substitute in the given information. m∠A+m∠C=90 26+C=90 Solve the equation. C=64 Check. 26+64=90 =90✓ The complement of the 26∘ angle is 64∘.

An angle measures 14∘. Find a. its supplement and b. its complement.

ANSWER supplement 166,complement. 76 Write the appropriate formula for the situation, and substitute in the given information. m∠A+m∠B=180 14+B=180 Solve the equation. B=166 Check. 14+166=180 =180 The supplement of the 14∘ angle is 166∘. b.Write the appropriate formula for the situation, and substitute in the given information. m∠A+m∠C=90 14+c=90 Solve the equation. C=76 Check. 14+76=90 The complement of the 14∘ angle is 76∘.