what is the measure of ∠adc in quadrilateral abcd?\n45°\n65°\n115°\n135°
what is the measure of ∠adc in quadrilateral abcd?\n45°\n65°\n115°\n135°
Answer
Explanation:
Step1: Identify the type of quadrilateral
The markings on the sides of the quadrilateral ABCD indicate that AB = CD and BC = AD, so it is an isosceles trapezoid. In an isosceles trapezoid, base - angles are equal and adjacent angles along a non - parallel side are supplementary.
Step2: Use the property of adjacent angles
Angle ∠BAD = 115°. Since ∠BAD and ∠ADC are adjacent angles along the non - parallel side AD of the isosceles trapezoid, and the sum of adjacent angles along a non - parallel side of an isosceles trapezoid is 180°. Let ∠ADC=x. Then ∠BAD + x=180°.
Step3: Solve for ∠ADC
We know that ∠BAD = 115°, so x = 180°−115° = 65°.
Answer:
65°