Question

Find the measure of arc CD, which is the value of y.

Question 12 options:

A) 48°


B) 73°


C) 59°


D) 146°

Answer 1

D) 146°

Explanation:

remember, the sum of all angles in any triangle is always 180°.

therefore, the angle at B is

180 - angle C - angle D = 180 - 59 - 48 = 73°.

now, the angle at the intersection of 2 chords of a circle is half of the sum of the arc angles in front and in the back of that angle.

in our case, the chords BC and BD intersect at B (directly on the circle arc itself).

so, the arc angle in front of the angle B is y. the arc angle in the back of the angle B is 0.

angle B = ½(y + 0) = y/2

73 = y/2

y = 146°