Question

The measure of angle XSN is 38° and the measure of angle YNP is 56°. What is the measure of angle SXN and angle SXV?

Answer 1

∠SXN = 108°; ∠SXV = 72°

Explanation:

∠SXN

∠YNP and ∠ QNX are vertically opposite angles, so

∠QNX = ∠YNP = 56°

∠QNX + ∠SNX = 90°

56 + ∠SNX = 90 Subtract 56 from each side

∠SNX = 34°

∠SNX + ∠XSN + ∠SXN = 180°

34 + 38 + ∠SXN = 180

72 + ∠SXN = 180 Subtract 72 from each side

∠SXN = 108°

∠SXV

∠SXN and ∠SXV are supplementary angles, so

∠SXN + ∠SXV = 180

108 + ∠SXV = 180 Subtract 108 from each side

∠SXV = 72°