Question

ACB is an isosceles triangle. ÐACB = 58°. Which of the pairs shown could be the measures of the other two angles?

A. ÐABC = 91°, ÐBAC = 59°

B. ÐABC = 59°, ÐBAC = 71°

C. ÐABC = 61°, ÐBAC = 61°

D. ÐABC = 78°, ÐBAC = 42°

Answer 1

The correct answer is c

Answer 2

C. ∠ABC = 61°, ∠BAC = 61°

Explanation:

The remaining two angles must be equal. C is the only choice showing equal angles.

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As a check, the angles must add to 180°, so you have ...

... 2∠A + 58° = 180°

... ∠A + 29° = 90° . . . . . . divide by 2

... ∠A = 61° = ∠B . . . . . . . matches choice C