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:
let A and D be two consecutive angle.
then, by the given condition
[tex]\angle A \cong \angle D[/tex] ......[1]
From the property of parallelogram:
Consecutive angles are supplementary
Then;
[tex]\angle A + \angle D = 180^{\circ}[/tex]
From equation [1];
[tex]\angle A + \angle A = 180^{\circ}[/tex]
Combine like terms :
[tex]2\angle A = 180^{\circ}[/tex]
Divide both sides by 2 we get;
[tex]\frac{2 \angle A}{2} = \frac{180^{\circ}}{2}[/tex]
Simplify:
[tex]\angle A = 90^{\circ}[/tex]
From the given property of parallelogram : if one of the angle is right, then all the angles in the parallelogram are right angle.
∴ [tex]\angle A = \angle B = \angle C = \angle D = 90^{\circ}[/tex]
Therefore, the measure of each angle is [tex]90^{\circ}[/tex]
