Question

ABCD is a parallelogram. Find the measures of angles B, C and D.

Answer 1

In a parallelogram ABCD, angle C=64, B=D=116.

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (they add up to 180 degrees). If angle A is given as 64 degrees in parallelogram ABCD, we can find the measures of the other angles using these properties.

Angle A = 64 degrees (given)

Angle C = Angle A = 64 degrees (Opposite angles are equal).

Angle B + Angle C = 180 degrees (Consecutive angles are supplementary).

Angle B + 64 = 180 degrees

Angle B = 180 - 64 = 116 degrees

Now, we have the measures of three angles in parallelogram ABCD:

Angle A = 64 degrees

Angle B = 116 degrees

Angle C = 64 degrees

To find angle D, we use the fact that consecutive angles in a parallelogram are supplementary:

Angle D + Angle C = 180 degrees

Angle D + 64 = 180 degrees

Angle D = 180 - 64 = 116 degrees

Therefore, in parallelogram ABCD:

Angle A = 64 degrees

Angle B = 116 degrees

Angle C = 64 degrees

Angle D = 116 degrees