In pentagon ABCDE, shown below, ∠A measures 50°. What is the total measure of the other 4 interior angles?
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
(C) Incorrect: this would be the measure of the other interior angles of a quadrilateral, 360°-50°=310°
(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°
