Answer:
see explanation
Explanation:
∠ 1 and 130° are a linear pair and sum to 180° , then
∠ 1 + 130° = 180° ( subtract 130° from both sides )
∠ 1 = 50°
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the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
130° is an exterior angle of the triangle on the left , then
∠ 2 + 90° = 130° ( subtract 90° from both sides )
∠ 2 = 40°
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∠ 2 and ∠ 3 are a linear pair and sum to 180° , then
∠ 2 + ∠ 3 = 180° , that is
40° + ∠ 3 = 180° ( subtract 40° from both sides )
∠ 3 = 140°
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∠ 2 and angle inside triangle on right are vertically opposite angles and are congruent (equal )
the triangle on the right has 2 congruent legs and is isosceles with base angles being congruent , then
∠ 5 = 40° ( equal to the vertically opposite angle in the triangle )
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the sum of the 3 angles in a triangle = 180° , then
∠ 4 + ∠ 5 + 40° = 180° , so
∠ 4 + 40° + 40° = 180°
∠ 4 + 80° = 180° ( subtract 80° from both sides )
∠ 4 = 100°
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in summary
∠ 1 = 50° , ∠ 2 = 40° , ∠ 3 = 140° , ∠ 4 = 100° , ∠ 5 = 40°