Question

If two consecutive angles of a parallelogram are congruent, what is the measure of each angle?

Answer 1

Answer:

Measure of each angle is 90 degree.

Step-by-step explanation:

Given : If two consecutive angles of a parallelogram are congruent.

To find the measure of each angle:

There are 6 important properties of parallelograms:

• Opposite sides are congruent.

• Opposite angles are congruent
• Consecutive angles are supplementary.
• If one of the angle is right angle, then all angles are right.
• Diagonals of a parallelogram bisect each other
• Also, each diagonal of a parallelogram separates it into two congruent.

let A and D be two consecutive angle.

then, by the given condition

$\angle A \cong \angle D$           ......[1]

From the  property of parallelogram:

Consecutive angles are supplementary

Then;

$\angle A + \angle D = 180^{\circ}$

From equation [1];

$\angle A + \angle A = 180^{\circ}$

Combine like terms :

$2\angle A = 180^{\circ}$

Divide both sides by 2 we get;

$\frac{2 \angle A}{2} = \frac{180^{\circ}}{2}$

Simplify:

$\angle A = 90^{\circ}$

From the given property of parallelogram : if one of the angle is right, then all the angles in the parallelogram are right angle.

∴ $\angle A = \angle B = \angle C = \angle D = 90^{\circ}$

Therefore, the measure of each angle is $90^{\circ}$