Holt CA Course Finding Angle Measures Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

Holt CA Course Finding Angle Measures 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

Holt CA Course Finding Angle Measures 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 Finding Angle Measures Objective: You will learn how to (YWLHT) use angle relationships to find angle measures.

Holt CA Course Finding Angle Measures Example 1: Finding an Unknown Angle Measure Find each unknown angle measure. Since the angles are complementary, the sum of the angle measures is 90 °. a 71° A. The angles are complementary.

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

Holt CA Course Finding Angle Measures a 125° B. The angles are supplementary. Since the angles are supplementary, the sum of the angle measures is 180 °. Example 2: Finding an Unknown Angle Measure Find each unknown angle measure.

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

Holt CA Course Finding Angle Measures a 82° C. The angles are vertical angles. Example 3: Finding an Unknown Angle Measure Find each unknown angle measure. Since the angles are vertical angles, the angles are congruent.

Holt CA Course Finding Angle Measures a m  a = 82° Congruent angles have the same measure. a 82° C. The angles are vertical angles. Example 3: Finding an Unknown Angle Measure Find each unknown angle measure. Since the angles are vertical angles, the angles are congruent.

Holt CA Course Finding Angle Measures The sum of the measures is 180°. D.  BEA   CED; m  AED = 180° a 31° E C B DA Example 4: Finding an Unknown Angle Measure Find each unknown angle measure.

Holt CA Course Finding Angle Measures a 31° + m  a + 31° = 180° –62° a 62° + m  a = 180° The sum of the measures is 180°. D.  BEA   CED; m  AED = 180° a m  a = 118° a 31° E C B DA Example 4: Finding an Unknown Angle Measure Find each unknown angle measure.

Holt CA Course Finding Angle Measures Check It Out! Example 5 Find each unknown angle measure. 65° + m  d = 90° –65° m  d = 25° Subtract 65° from both sides. d 65° A. The angles are complementary. Since the angles are complementary, the sum of the angle measures is 90 °.

Holt CA Course Finding Angle Measures Check It Out! Example 6 Find each unknown angle measure. 145° + m  s = 180° –145° m  s = 35° Subtract 145° from both sides. s 145° B. The angles are supplementary. Since the angles are supplementary, the sum of the angle measures is 180 °.

Holt CA Course Finding Angle Measures Check It Out! Example 7 Find each unknown angle measure. m  t = 32° Congruent angles have the same measure. t 32° C. The angles are vertical angles. Since the angles are vertical angles, the angles are congruent.

Holt CA Course Finding Angle Measures 25° + b + 25° = 180° –50° –50° 50° + b = 180° The sum of the measures is 180°. D.  WZV   XZY; m  VZY = 180° b = 130° Check It Out! Example 8 Find each unknown angle measure. b 25° Z X W YV

Holt CA Course Finding Angle Measures Home Learning On-Line Tutoring Geo-match-try Geo-fit Geo-Vocab Shape Quiz Geo-Terms

Holt CA Course Finding Angle Measures –27° 27 ° + c = 90° The sum of the measures is 90°. c = 63° Subtract 27° from both sides. Example 9: 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.

Holt CA Course Finding Angle Measures –151° 151 ° + a = 180° The sum of the measures is 180°. a = 29° Subtract 151° from both sides. Example 9 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.

Holt CA Course Finding Angle Measures b = 27°Vertical angles are congruent. Example 9 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.

Holt CA Course Finding Angle Measures –22° 22 ° + z = 90° z = 68° Check It Out! Example 10 Use the information in the diagram to find the unknown angle measures x, y, and z. Show your work. x 165° 22° z y Step 1: The angles labeled z and 22 ° are complementary. To find z, use properties of complementary angles.

Holt CA Course Finding Angle Measures –165° 165 ° + x = 180° x = 15° Check It Out! Example 10 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. x 165° 22° z y

Holt CA Course Finding Angle Measures y = 22° Check It Out! Example 10 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. x 165° 22° z y

Holt CA Course Finding Angle Measures

Holt CA Course Finding Angle Measures

Holt CA Course Finding Angle Measures Home Learning On-Line Tutoring Geo-match-try Geo-fit Geo-Vocab Shape Quiz Geo-Terms

Holt CA Course Finding Angle Measures Lesson Quiz: Part I Find each unknown angle measure. 1. The angles are vertical angles. 2. The angles are supplementary. d = 130° x = 45°

Holt CA Course Finding Angle Measures Lesson Quiz: Part II p = 78° 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. ̃ a = 147°, b = 123°, c = 19°