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

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

          ......[1]

From the  property of parallelogram:

Consecutive angles are supplementary

Then;

From equation [1];

Combine like terms :

Divide both sides by 2 we get;

Simplify:

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

∴

Therefore, the measure of each angle is

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation:

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step-by-step explanation: