Answer:
∠ WXZ = 74° , ∠ XZW = 68°
Explanation:
the sum of the 3 angles in a triangle = 180°
(a)
Consider Δ XYZ
∠ ZXY + 54° + 20° = 180°
∠ ZXY + 74° = 180° ( subtract 74° from both sides )
∠ ZXY = 106°
∠ WXZ and ∠ ZXY are a linear pair and sum to 180° , that is
∠ WXZ + ∠ ZXY = 180°
∠ WXZ + 106° = 180° ( subtract 106° from both sides )
∠ WXZ = 74°
(b)
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles
∠ ZXY is an exterior angle of Δ WXZ , then
∠ XZW + 38° = ∠ ZXY ( substitute values )
∠ XZW + 38° = 106° ( subtract 38° from both sides )
∠ XZW = 68°