Answer: A. 38, 142
Step-by-step 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,
[tex]\angle 1 = \frac{36^{\circ}+40^{\circ}}{2}=\frac{76}{2}=38^{\circ}[/tex]
⇒ ∠ 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.
