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Learn how to apply the Triangle Sum and Exterior Angle Theorems to find missing angle measures in triangles. Practice solving problems using these theorems.
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1/5: Apply the triangle sum theorem & exterior angle theorem to solve for missing angle measures.
Apply the triangle sum theorem & exterior angle theorem to solve for missing angle measures. When you finish Do Now: • Flip Over • Write down objective • Complete warm-up
E 87⁰ 180 - 145 145⁰ 58⁰ 35⁰ m∠DFE= 35 ⁰ 58 + 35 + ∠DEF = 180 m∠DEF = 87⁰ 145⁰ 145⁰ When you add the two non-adjacent interior angles together, you get the measure of the exterior angle.
The sum of the three interior angle measures of any triangle is equal to 180⁰ In + In + In = 180 The sum of the two nonadjacent interior angle measures of any triangle is equal to the measure of the exterior angle. In + In = Out
Triangle Exterior Angle Theorem In + In = Out 30 + 42 = m∠2 72⁰ 108⁰ m∠2 = 72⁰ Obtuse Triangle
Triangle Exterior Angle Theorem In + In = Out 75⁰ 145⁰ 35⁰ x + 70 = 2x – 5 + 5 + 5 x + 75 = 2x m∠JKM = 2x – 5 -x -x m∠JKM = 2(75) – 5 75 = x m∠JKM = 145⁰ Acute Triangle
