Question

Given: m arc AB = 4x, m arc BC = 3x
m arc CD = 2x, m arc DA = 3x
Find: m∠APB

Answer 1

30°

Explanation:

The addition of the arcs AB, BC, CD and DA is equal to 360°

4x + 3x +2x +3x = 360°

12x = 360°

x = 360°/12

x = 30°

Then:

m arc AB = 4*30° = 120°

m arc CD = 2*30° = 60°

The following relation must be satisfied:

m∠APB = 1/2*(m arc AB - m arc CD)

m∠APB = 1/2*(120° - 60°)

m∠APB = 30°