Question

Find the values of x and y that make the quadrilateral a parallelogram

Answer 1

For given parallelogram, the value of x = 114° and y = 66°

Explanation:

(Refer figure)

Given quadrilateral ABCD is a parallelogram.

m∠A = 66°

m∠B = x°

m∠C = y°

m∠D = 114°

Since by properties of parallelogram, the both pairs of opposite sides of a parallelogram are parallel.

Opposite angles of a parallelogram are congruent ...........................(1)

Consecutive angles of a parallelogram are supplementary ................(2)

Using (1) for given parallelogram ABCD; we get,

m∠B = m∠D

m∠A = m∠C

Therefore x = 114° and y = 66°.

Using (2) to check whether the two consecutive angles are supplementary.

( m∠A + m∠D ) =  ( m∠B + m∠C ) = ( m∠C + m∠D ) = 66° + 114° = 180°