Question

Circle X is shown in the diagram.

Circle X is shown. 2 chords intersect at a point to form arcs a and b. Arc a is intercepted by angle 1. Arc b is intercepted by angle 2. Arcs d and c are the other 2 arcs.

Which equation can be used to solve for m∠1?

m∠1 = One-half(a – b)
m∠1 = One-half(a + b)
m∠1 = One-half(c – d)
m∠1 = One-half(c + d)

Answer 1

m∠1 = 1/2(a + b)

Reason: When two chords intersect inside a circle, the measure of an angle formed is half the sum of the measures of the intercepted arcs (the arc intercepted by the angle and the arc intercepted by its vertical opposite angle). Here those arcs are a and b.