Question

Prove that opposite angles of an isosceles trapezium are supplementary

Answer 1

Let ABCD be an isosceles trapezoid with AB being one of the bases and CD being the other base. 

<A + <D = 180 

<B + <C = 180 

<A = <B because the trapezoid is isosceles. 

Therefore, 

<B + <D = 180 and 

<A + <C = 180 

Therefore, opposite angles <B and <D are supplementary, and opposite angles <A and <C are supplementary. 

Therefore, an isosceles trapezoid's opposite angles are supplementary.