Question

.If an exterior angle of a triangle is 65° and one of the opposite interior angle to it is 35° then other two angles are​

Answer 1

Answer:

∠A = 30° and ∠B = 115°

Step-by-step explanation:

Please refer to the picture below that I am using for my reference and please change the name of the angles in the answer according to your markings.

Given: ∠D = 65°, ∠C = 35°, ∠A=?, ∠B = ?

∠A + ∠C = ∠D (Exterior Angle Property)

∠A + 35 = 65 ( substitute from given)

∠A = 65 - 35

∴ ∠A = 30° -----> (1)

∠A + ∠B + ∠C = 180°  ( Angle Sum property)

30 + ∠B + 35 = 180  ( substitute fro (1) & given)

65 +∠B = 180

∠B = 180 - 65

∴ ∠B = 115°

OR

∠B + ∠D = 180   ( Linear Pair )

∠B + 65 = 180

∠B = 180 - 65

∴ ∠B = 115°

Hence ∠A = 30° and ∠B = 115°

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