Question

For the given quadrilateral, find the angle $\angle D.$

degrees

Answer 1

The given quadrilateral is an isosceles trapezoid.

Considering AB as transversal to AD and BC, $\angle A$ and $\angle B$ are supplementary angles.

$\therefore \angle A={180}^o-\angle B={72}^o$

An isosceles trapezoid is formed by cutting an isosceles triangle along a line parallel to the side of the triangle connecting the equal angles of the triangle.

That means the non-parallel equal lines of an isosceles trapezoid, when extended, always meet at a point, forming an isosceles triangle.
$\therefore \angle A=\angle D={72}^o$