Questions: What is the measure of angle D?

What is the measure of angle D?
Transcript text: What is the measure of angle D ?
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Solution

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Solution Steps

Step 1: Identify the given information

The figure ABCD is an isosceles trapezoid, where AB is parallel to DC. Angle D is (2x + 27)° and angle C is (5x - 12)°.

Step 2: Set up an equation

In an isosceles trapezoid, the base angles are congruent. Therefore, angle D is congruent to angle C. This gives us the equation: 2x + 27 = 5x - 12

Step 3: Solve for x

Subtract 2x from both sides: 27 = 3x - 12 Add 12 to both sides: 39 = 3x Divide both sides by 3: x = 13

Step 4: Find the measure of angle D

Substitute x = 13 into the expression for angle D: 2(13) + 27 = 26 + 27 = 53

Final Answer

53°

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