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California Standards

California Standards. 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.

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California Standards

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  1. California Standards 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

  2. 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°.

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

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

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

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

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

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

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

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

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