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8-3 Angle Relationships Preview Warm Up California Standards Lesson Presentation Holt CA Course 1 8-3 Angle Relationships Warm Up Complete each sentence. 1. Angles whose measures have a sum of 90° are _______________ . complementary 2. A part of a line that starts at one point and ray extends forever in one direction is called a _______. 3. Angles whose measures have a sum of 180° are supplementary ______________. 4. A part of a line between two points is called a segment ____________. Holt CA Course 1 8-3 Angle Relationships California Standards Review of Grade 6 MG2.2 Use properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Also covered: 6MG2.1 Holt CA Course 1 8-3 Angle Relationships Additional Example 1: Finding Angle Measures Use the diagram to find each angle measure. A. If m1 = 37°, find m 3. 1 and 2 are supplementary. m2 = 180° – 37° = 143° The measures of 2 and 3 are supplementary. m3 = 180° – 143° = 37° So m1 = m3, or 1 3. Holt CA Course 1 8-3 Angle Relationships Writing Math ~ which is read as The symbol for congruence is =, “is congruent to.” Holt CA Course 1 8-3 Angle Relationships Additional Example 1: Finding Angle Measures Use the diagram to find each angle measure. B. If m4 = y°, find m2. 3 and 4 are supplementary. m3 = 180° – y° 2 and 3 are supplementary. m2 = 180° – m3 o – yo Substitute 180 = 180° – (180o – yo) for m3. = 180° – 180° + y° Distributive Property = y° Simplify. So m4 = m2, or 4 2. Holt CA Course 1 8-3 Angle Relationships Check It Out! Example 1 Use the diagram to find each angle measure. 2 A. If m1 = 42°, find m3. 1 3 4 The measures of 1 and 2 are supplementary. m2 = 180° – 42° = 138° The measures of 2 and 3 are supplementary. m3 = 180° – 138° = 42° So m1 = m3, or 1 3. Holt CA Course 1 8-3 Angle Relationships Check It Out! Example 1 Use the diagram to find each angle measure. B. If m4 = x°, find m2. 3 and 4 are supplementary. m3 = 180° – x° 2 and 3 are supplementary. 2 1 3 4 m2 = 180° – m3 o – xo Substitute 180 = 180° – (180o – xo) for m3. = 180° – 180° + x° Distributive Property = x° Simplify. So m4 = m2, or 4 2. Holt CA Course 1 8-3 Angle Relationships The angles in Example 1 are examples of adjacent angles and vertical angles. These angles have special relationships because of their positions. Adjacent angles have a common vertex and a common side, but no common interior points. Vertical angles are the nonadjacent angles formed by two intersecting lines. Holt CA Course 1 8-3 Angle Relationships A transversal is a line that intersects two or more lines that lie in the same plane. Transversals to parallel lines form angle pairs with special properties. Holt CA Course 1 8-3 Angle Relationships Holt CA Course 1 8-3 Angle Relationships Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line of the angle. l || line m. Find the measure A. 4 Corresponding angles are congruent. m4 = 124° Holt CA Course 1 8-3 Angle Relationships Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line of the angle. l || line m. Find the measure B. 2 2 is supplementary to the 124° angle. m2 + 124° = 180° –124° m2 Holt CA Course 1 –124° Subtract. = 56° Simplify. 8-3 Angle Relationships Additional Example 2: Finding Angle Measures of Parallel Lines Cut by Transversals In the figure, line of the angle. C. 6 l || line m. Find the measure 2 and 6 are corresponding angles. m6 = 56° Holt CA Course 1 8-3 Angle Relationships Check It Out! Example 2 In the figure, line of the angle. A. 7 l || line m. Find the measure Alternate exterior angles are congruent. m7 = 144° 1 Holt CA Course 1 144° 3 4 5 6 7 8 m n 8-3 Angle Relationships Check It Out! Example 2 In the figure, line of the angle. B. 1 l || line m. Find the measure 1 is supplementary to the 144° angle. m1 + 144° = 180° –144° –144° m 1 = 36° Holt CA Course 1 1 144° 3 4 5 6 7 8 m n 8-3 Angle Relationships Check It Out! Example 2 In the figure, line of the angle. l || line m. Find the measure C. 6 Corresponding angles are congruent. m6 = 144° Holt CA Course 1 1 144° 3 4 5 6 7 8 m n 8-3 Angle Relationships Lesson Quiz In the figure, line a || line b. 1. Name all angles congruent to 3. 1, 5, 7 2. Name all the angles supplementary to 6. 1, 3, 5, 7 3. If m1 = 105° what is m3? 105° 4. If m5 = 120° what is m2? 60° Holt CA Course 1