Question

Find the measure of c. A. 120 B. 140 C. 160 D. 180

Answer 1

Answer:

B. 140

Step-by-step explanation:

A radius is a segment connecting the center of a circle to the outer perimeter of the circle. One property of radii is that all radii from the same circle are congruent. Thus, one can conclude that the triangle with the angle (C) is an isosceles triangle because its sides are radii of the same circle, thus they must be congruent.

One property of an isosceles triangle is the base angle theorem. This states that the angles opposite the congruent sides in an isosceles triangle are cognrunet. Moreover, a property of all triangles is that the sum of angles in any triangle is (180) degrees. Therefore, one can combine this information with the base angles theorem to form an equation and solve for the unknown, (C).

20  + 20 + (m<C) = 180

Simplify,

40 + m<C = 180

Inverse operations,

m<C = 140