Answer:
∠ 1 = 109° , ∠ 2 = 29° , ∠ 3 = 71°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , then
∠ 1 + 35° + 36° = 180°
∠ 1 + 71° = 180° ( subtract 71° from both sides )
∠ 1 = 109°
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∠ RVU and ∠ 1 are adjacent angles on a straight line and sum to 180° , then
∠ RVU + ∠ 1 = 180°
∠ RVU + 109° = 180° ( subtract 109° from both sides )
∠ RVU = 71°
In Δ RVU
∠ 2 + 80° + 71° = 180° ( sum of angles in triangle )
∠ 2 + 151° = 180° ( subtract 151° from both sides )
∠ 2 = 29°
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∠ 3 and ∠ RVU are vertically opposite angles and are congruent , then
∠ 3 = 71°
