Question

ABCD is cyclic quadrilateral which AB||CD. If angle B is 65°, then find other angles pf the quadrilateral.

Answer 1

Dear Student,
Here is the answer to your question.
It is given that ABCD is a cyclic quadrilateral where AB||DC.
It is known that opposite angles of a cyclic quadrilateral are supplementary.
∴∠B + ∠D = 180°
⇒ 65°+ ∠D = 180°
⇒ ∠D = 180 °– 65°= 115°
It is also given that AB||DC.
When two parallel lines are intersected by a transversal, the interior angles on the same side of the transversal are supplementary.
So, ∠B + ∠C = 180° and ∠D + ∠A = 180°
∠B + ∠C = 180°
⇒ 65°+ ∠C = 180°
⇒ ∠C = 180° – 65° = 115°
∠D + ∠A = 180°
⇒ 115° + ∠A = 180°
⇒ ∠A = 180° – 115° = 65°

Thus, ∠B = 65° = ∠A, ∠D = 115° = ∠C

Note: Quadrilateral ABCD is a trapezium.
Cheers!