Question

The adjacent angles ∠1 and ∠2 have measures of

A.38, 142
B.76, 104
C.28, 152

Answer 1

1+2=180
1=3=(36+40)/2=38
2=180-38=142
So correct answer is C

Answer 2

Answer: A. 38, 142

Explanation:

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,

`\angle 1 = (36^(\circ)+40^(\circ))/(2)=(76)/(2)=38^(\circ)`

⇒ ∠ 1 = 38°

Now, again by the diagram,

∠1 and ∠2 are linear pairs,

⇒ ∠1 + ∠2 = 180°

⇒ 38° + ∠2 = 180°

⇒ ∠2 = 142°

Hence, Option A is correct.