ACT Question for September 25th

In pentagon ABCDE, shown below, ∠A measures 50^°. What is the total measure of the other 4 interior angles?

A) 130^°

B) 200^°

C) 310^°

D) 432^°

E) 490^°

CORRECT

INCORRECT

The correct answer is (E).

Getting to the Answer: The sum of the interior angles of a polygon is 180^°(n-2), where n is the number of sides of the polygon. The figure ABCDE has five sides, so the total measure of the interior angles is 180^°(5-2)=180^°(3)=540^°. The sum of the remaining interior angles is therefore 540^°-50^°=490^°.

(A) Incorrect: this would be the measure of the other interior angles of a triangle, 180^°-50^°=130^°

(B) Incorrect: this multiplies 50^° by 4

(D) Incorrect: this is ⁴⁄₅(540^°), which is the sum of the measures of four angles of a pentagon with five equal angles; however, angle A is 50^°, not 108^°

(E) Correct: this matches the correct calculation

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ACT Question for September 25th

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