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Find the measures of the numbered angles in the isosceles trapezoid. Please explain how you got your answer.

Find the measures of the numbered angles in the isosceles trapezoid. Please explain-example-1

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Answer:

∠ 1: 71°

∠ 2: 109°

∠ 3: 109°

Explanation:

The first angle I found was angle 3:

We can draw a straight line down through the middle of the trapezoid. That creates a quadrilateral for us, and since both the top and bottom lines were parallel, we have 3 angles already. The given angle is 71 and since we drew a perpendicular line through the middle of the parallel lines, the two angles of the perpendicular line are both 90 degrees.

The sum of all angles within a quadrilateral = 360 degrees

71° + 90° + 90° + ∠ 3 = 360°

∠ 3 = 360° - 90° - 90° - 71°

∠ 3 = 109°

Since the trapezoid is isosceles, opposite angles must be supplementary, meaning that they must add up to 180 degrees.

Angle 2

∠ 2 + 71° = 180°

∠ 2 = 109°

Angle 1

∠ 1 + 109° = 180°

∠ 1 = 71°

User Sunny Moon
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