Holt CA Course 1 9-7 Angle Measures in Triangles MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle.

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Holt CA Course Angle Measures in Triangles MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Also covered: AF1.1, MG2.1 California Standards

Holt CA Course Angle Measures in Triangles If you tear off the corners of a triangle and put all three of them together, you will find that they form a straight angle. This suggests that the sum of the measures of the angles in a triangle is 180°.

Holt CA Course Angle Measures in Triangles Angles of a Triangle The sum of the measures of the angles in a triangle is 180°. m1 + m2 + m3 = 180° 1 3 2

Holt CA Course Angle Measures in Triangles A. Find the unknown angle measure in each triangle. Additional Example 1: Finding an Angle Measure of in a Triangle 55° 80° x 80° + 55° + x = 180° 135° + x = 180° –135° x = 45° The measure of the unknown angle is 45°. The sum of the angle measures in a triangle is 180°. Add 55° and 80°. Subtract 135° from both sides.

Holt CA Course Angle Measures in Triangles B. Find the unknown angle measure in each triangle. Additional Example 1: Finding an Angle Measure of in a Triangle 34° x 34° + 90° + x = 180° 124° + x = 180° –124° x = 56° The measure of the unknown angle is 56°. The sum of the angle measures in a triangle is 180°. Add 34° and 90°. Subtract 124° from both sides.

Holt CA Course Angle Measures in Triangles A. Find the unknown angle measure in the triangle. Check It Out! Example 1 90° + 30° + x = 180° 120° + x = 180° –120° x = 60° The measure of the unknown angle is 60°. The sum of the angle measures in a triangle is 180°. Add 30° and 90°. Subtract 120° from both sides. 30° x

Holt CA Course Angle Measures in Triangles B. Find the unknown angle measure in each triangle. Check It Out! Example 1 22° x 22° + 90° + x = 180° 112° + x = 180° –112° x = 68° The measure of the unknown angle is 68°. The sum of the angle measures in a triangle is 180°. Add 22° and 90°. Subtract 112° from both sides.

Holt CA Course Angle Measures in Triangles The figure shows part of the support structure of a bridge. Find the unknown angle measure x. Show your work. 75° 110° x Substitute 110° for mDEC. Subtract 110° from both sides. Step 1: Find the measure of DEA. mDEA + mDEC = 180 ° mDEA ° = 180 ° mDEA = 70 ° AB C D E Additional Example 2: Application

Holt CA Course Angle Measures in Triangles The figure shows part of the support structure of a bridge. Find the unknown angle measure x. Show your work. Additional Example 2 Continued x Sum of angle measures is 180°. Add 70° and 75°. Step 2: Find the angle measure x. 70 ° + 75 ° + x = 180 ° 145 ° + x = 180 ° x = 35 ° AB C D E Subtract 145° from both sides. 75° 110°

Holt CA Course Angle Measures in Triangles The figure shows a diagram of a design. Find the unknown angle measure x. Show your work. 65° 95° x Substitute 95° for mDEA. Subtract 95° from both sides. Step 1: Find the measure of DEC. mDEC + mDEA = 180 ° mDEC + 95 ° = 180 ° mDEC = 85 ° AB C D E Check It Out! Example 2

Holt CA Course Angle Measures in Triangles Check It Out! Example 2 Continued Sum of angle measures is 180 °. Add 85 ° and 65 °. Step 2: Find the angle measure x. 85 ° + 65 ° + x = 180 ° 150 ° + x = 180 ° x = 30 ° Subtract 150 ° from both sides. 65° 95° x AB C D E The figure shows a diagram of a design. Find the unknown angle measure x. Show your work.