Question

A parallelogram has one angle that measures 135 degrees. What are the measures of other three angles in the parallelogram?

Answer 1

Answer:

The measure of other three angles are 135° , 45° and 45°

Step-by-step explanation:

The opposite angles of a parallelogram are equal.

So if we consider a parallelogram ABCD ,

Angle A = Angle C

Angle B = Angle D

If we take angle A = 135° then angle C = 135°

SUM OF INTERIOR ANGLES OF A QUADRILATERAL IS 360°.

A+B+C+D=360°

135°+B+135°+D=360°

270°+B+D=360°

But B=D

So,2B=90°

B=45°

D=45°

So A = C = 135°

A = C = 135° B = D = 45°

A = C = 135° B = D = 45°

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Answer 2

Answer:

The measure of other three angles are 135° , 45° and 45°.....

Step-by-step explanation:

The opposite angles of a parallelogram are equal.

So if we consider a parallelogram ABCD ,

Angle A = Angle C

Angle B = Angle D

If we take angle A = 135° then angle C = 135°

SUM OF INTERIOR ANGLES OF A QUADRILATERAL IS 360°.

A+B+C+D=360°

135°+B+135°+D=360°

270°+B+D=360°

But B=D

So,2B=90°

B=45°

D=45°