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

The required angle in quadrilateral is m∠B = 114° , m∠C= 66°.

Given that,

ABCD is a parallelogram.

m∠A = 66°, m∠B = x°,  m∠C = y° , m∠D = 114°

According to the question,

Opposites sides of a parallelogram are equal and parallel to each other. All the angles of a parallelogram add up to 360degree.

∠A + ∠B + ∠C + ∠D = 360°.

Opposite angles of a parallelogram are congruent,

And Consecutive angles of a parallelogram are supplementary.

Therefore,

In the parallelogram ABCD,

m∠B = m∠D

m∠A = m∠C

Therefore, The value of m∠D = 114°, m∠A = 66°

From equation 1 and 2 ,

m∠B = m∠D

m∠A = m∠C

Then,

m∠B = 114°

m∠C = 66°

Hence, The required angle in quadrilateral is m∠B = 114° , m∠C= 66°.

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

(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°