Question

I’ve been stuck can someone explain

Answer 1

Option (3)

Explanation:

From the figure attached,

AB and CD are two chords intersecting at O.

m∠AOD = 37°

m∠AOC + m∠AOD = 180° [Since these angles are supplementary angles]

m∠AOC = 180° - 37°

= 143°

By the theorem of intersecting chords,

Measure of angle formed is the half of the sum of measures of the arcs intercepted by the angle and vertical angle.

m∠AOC =
`(1)/(2)(\widehat{AC}+\widehat{BD})`

143° =
`(1)/(2)[(x+5)+(x-5)]`

143° = x

Therefore, Option (3) will be the answer.