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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Tell whether the given angles are vertical, complementary, or supplementary. 1.  QXT and  QXR 2.  QXR and  TXS 3.  PXQ and  QXR 4.  PXQ and  PXS 5.  TXS and  SXR. supplementary. vertical.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. Warm Up Tell whether the given angles are vertical, complementary, or supplementary. 1.QXT and QXR 2. QXR and TXS 3. PXQ and QXR 4. PXQ and PXS 5.TXS and SXR supplementary vertical complementary supplementary supplementary

  3. 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

  4. Additional Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. A. The angles are complementary. Since the angles are complementary, the sum of the angle measures is 90°. 71° + m1 = 90° Subtract 71° from both sides. 1 –71°–71° m1 = 19° 71°

  5. Additional Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. B. The angles are supplementary. Since the angles are supplementary, the sum of the angle measures is 180°. 125° + m2 = 180° Subtract 125° from both sides. –125°–125° m2 = 55° 125° 2

  6. Additional Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. C. The angles are vertical angles. Since the angles are vertical angles, the angles are congruent. Congruent angles have the same measure. m3 = 82° 3 82°

  7. C B 4 31° A E D Additional Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. D. BEA CED; mAED = 180° Since BEA and CED are congruent, mCED = 31°. mBEA + mBEC + mCED = 180°. The sum of the measures is 180°. 31° + m4 + 31° = 180° Substitute. 62°+ m4 = 180° Add. –62°–62° Subtract 62° from both sides. m4 = 118°

  8. Check It Out! Example 1 Find each unknown angle measure. A. The angles are complementary. Since the angles are complementary, the sum of the angle measures is 90°. 65° + md = 90° d Subtract 65° from both sides. –65°–65° md = 25° 65°

  9. Check It Out! Example 1 Find each unknown angle measure. B. The angles are supplementary. Since the angles are supplementary, the sum of the angle measures is 180°. 145° + ms = 180° Subtract 145° from both sides. –145°–145° ms = 35° 145° s

  10. Check It Out! Example 1 Find each unknown angle measure. C. The angles are vertical angles. Since the angles are vertical angles, the angles are congruent. Congruent angles have the same measure. mt = 32° t 32°

  11. Check It Out! Example 1 Find each unknown angle measure. D. WZV XZY; mVZY = 180° X W b Since WZV and XZY are congruent, mXZY = 25°. mWZV + mWZX + mXZY = 180° 25° V Z Y The sum of the measures is 180°. 25° + b + 25° = 180° Substitute. 50°+ b = 180° Add. Subtract 50° from both sides. –50°–50° b = 130°

  12. Additional Example 2: Application Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work. Step 1: The angles labeled c and 27° are complementary. To find c, use properties of complementary angles. The sum of the measures is 90°. 27°+ c = 90° –27°–27° Subtract 27° from both sides. c = 63°

  13. Additional Example 2 Continued Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work. Step 2: The angles labeled a and 151° are supplementary. To find a, use properties of supplementary angles. The sum of the measures is 180°. 151°+ a = 180° –151°–151° Subtract 151° from both sides. a = 29°

  14. Additional Example 2 Continued Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work. Step 3: The angles labeled b and 27° are vertical angles. To find b, use properties of vertical angles. b = 27° Vertical angles are congruent.

  15. 165° y x 22° z Check It Out! Example 2 Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work. Step 1: The angles labeled z and 22° are complementary. To find z, use properties of complementary angles. The sum of the measures is 90°. 22°+ z = 90° –22°–22° Subtract 22° from both sides. z = 68°

  16. 165° y x 22° z Check It Out! Example 2 Continued Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work. Step 2: The angles labeled x and 165° are supplementary. To find x, use properties of supplementary angles. The sum of the measures is 180°. 165°+ x = 180° –165°–165° Subtract 165° from both sides. x = 15°

  17. 165° y x 22° z Check It Out! Example 2 Continued Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work. Step 3: The angles labeled y and 22° are vertical angles. To find y, use properties of vertical angles. y = 22° Vertical angles are congruent.

  18. Lesson Quiz: Part I Find each unknown angle measure. 1. The angles are vertical angles. 2. The angles are supplementary. d = 130° x = 45°

  19. Lesson Quiz: Part II 3.KNL = LNM; mJNM = 180° 4. Use the information in the diagram to find the unknown angle measures a, b, and c. Show your work. ̃ p = 78° a = 147°, b = 123°, c = 19°

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