Question

The adjacent angles ∠1 and ∠2 have measures of _______?

1) 38
2) 142
3) 76
4) 104
5) 28
6) 152

Answer 1

The adjacent angles ∠1 and ∠2 have measures of A. 38, 142.

By the Angles of Intersecting Chords Theorem, When two chords intersect inside a circle, then the measure of the angle formed is one half the sum of chord's intercepted arcs.

Thus, by the given diagram,

∠1 = 76/2

⇒ ∠ 1 = 38°

Now, again by the diagram,

∠1 and ∠2 are linear pairs,

⇒ ∠1 + ∠2 = 180°

⇒ 38° + ∠2 = 180°

⇒ ∠2 = 142°