Question

Find the measure of arc AC, please show the work.

Answer 1

100°

Explanation:

ARC AC is DOUBLE of the angle ABF (inscribed angle theorem).

The sum of 3 angles in a triangle is 180°.

Now, in Triangle ABF, AFB = 25, BAF = 105. that leaves us with angle ABF (or B). Thus, we can write:

AFB + BAF + ABC = 180

25 + 105 + ABF = 180

130 + ABF = 180

ABF = 180 - 130 = 50 (Angle B)

We know Arc AC is double of Angle ABF, so Arc AC = 2 * 50 = 100.

Arc AC = 100°

Answer 2

The correct answer is,

mAC = 100°

Explanation:

From the figure we get,

m<AFB = 25° and m<BAF = 105°

We can write,

m<AC = 2 * <ABC

To find the value of m<ABC

m<ABC = 180 - ( m<AFB + m<BAF) angle sum property

= 180 - ( 25 + 105)

= 180 - 130 = 50

m<ABC = 50°

To find the value of mAC

mAC = 2 * m<ABC = 2 * 50 = 100°

Therefore correct answer is mAC = 100°