Question

*****PLEASE HELP*****

Given the figure, if ∠ABC is 20° and C is the center of the circle, what is the measure of the central angle ∠ACB?


A) 40°

B) 70°

C) 100°

D) 140°

Answer 1

D

Explanation:

The triangle is an isosceles triangle (2 sides same).

The sides BC and AC are radius of the circles, so these 2 sides are congruent. So, the opposite angles are equal as well. Since one angle is given as 20, the other angle is also 20.

So, we have the three angles of the triangle as:

20, x, and 20

We know, sum of 3 angles of a triangle is 180, thus we can write:

20 + x + 20 = 180

Now, we solve for x:

20 + x + 20 = 180

40 + x = 180

x = 180 - 40

x = 140

Correct answer is D