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Angles of Triangles The angles inside a polygon are called interior angles. When the sides of a polygon are extended, other angles are formed. The angles outside the polygon that are adjacent to the interior angles are called exterior angles. The sum of the interior angle measures of a triangle is 180°. ∠𝐴 + ∠𝐵 + ∠𝐶 = 180° To find the measure of an interior angle of a triangle: 𝑥 + 29° 90° 𝑥° Step 1 – Copy the formula ∠𝐴 + ∠𝐵 + ∠𝐶 = 180° Step 2 – Fill in the values known 90° + (𝑥 + 29)° + 𝑥° = 180° Step 3 - Solve 119 + 2𝑥 = 180 −119 − 119 2𝑥 = 61 2𝑥 2 61 = 2 𝑥 = 30.5 The measures of the 3 angles are: 90° 30.5° 30.5 − 29 = 59.5° This answer can be checked by adding all 3 angles: 90 + 30.5 + 59.5 = 180 MA08 3-2 To find the measure of an exterior angle of a triangle: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. 𝑥° ∠𝑧 = ∠𝑥 + ∠𝑦 𝑦° 𝑧° Example: Find the measure of ∠𝑧 87° 51.8° 𝑧° Step 1 – Copy the formula ∠𝑧 = ∠𝑥 + ∠𝑦 Step 2 – Fill in the values known 𝑧 = 87 + 51.8 Step 3 - Solve 𝑧 = 138.8 The measure of ∠𝑧 𝑖𝑠 138.8° MA08 3-2