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Warm up: Replace the with <, >, or =. B A 45° 45° 135° C D 1. AB BC 2. m A m B 3. m BCA m A 4. AD AC 5. m A m BCD OBJECTIVE: You will learn to identify exterior angles and remote interior angles of a triangle and use the Exterior Angle Theorem. Section 72 _____________________ D 3 exterior angle 1 G F 2 4 E remote interior angle 1 11 12 10 2 4 1 5 6 3 9 7 8 Example 1: Name the remote interior angles with respect to 1. 1 2 3 4 5 Example 2: In the figure, 2 and 3 are remote interior angles with respect to what angle? 2 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. m 1 = m 3 + m 4 D 3 1 G 2 F 4 E Example 3: If m 2 = 38 and m 4 = 134, what is m 5? 56 1 2 3 4 Example 4: If m 2 = x + 17, m 3 = 2x, and m 6 = 101, find the value of x. 3 Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either of its two remote interior angles. m 1 > m 3 and m 1 > m 4 D 3 1 G 2 4 F E Theorem 75 If a triangle has one right angle, then the other two angles must be acute. Example 5: Name two angles in MAL that have measures less than 90. M 1 3 C L 2 A 4 Guided Practice: 1. Draw a triangle and extend all of the sides. Identify an exterior angle at each of the vertices. A X 1 2 B 3 4 5 K L 2. Name two remote interior angles with respect to AKL. 3. If m 3 = 65 and m 5 = 142, what is m 2? 4. If m 1 = 2x 26, m 3 = x, and m 4 = 37, find the value of x. 5. Replace with <, >, or = to make a true sentence. m 3 m 1 5 Do you have any Vocab questions? OBJECTIVE: HOMEWORK: p. 286 287 # 8 22 ***Quiz next time over section 71*** 6