Answer to Question #197462 in Geometry for Andu

Question

The trapezoid ABCE consists of the parallelogram ABCD and the right-angled triangle ADE. Find the measure of the angle AED. The angle of the parallelogram ABC is 110⁰

Answer 1

Here it is given that the quadrilateral ABCE is a trapezoid and ABCD is a parallelogram. And it is also give that the angle ∠ABC=110° Then in the parallelogram ABCD the opposite angle ∠ADC would also be 110° as opposite angle of a parallelogram are equal. From the above information the trapezoid is plotted as shown in the figure.

 

Now if ∠ADC=110° , then its corresponding side ∠ADE

will be;∠ADE=180°-110° =70°

=70°

Now its is given that ∆ADE is a right triangle. From the figure ∠EAD cannot be 90° since it is an acute angle. Therefore ∠AED=90°

Hence;

∠EAD=180° -90° -70° =20°

=20°

Therefore ∠AED=90°