Question

If one angle of a parallelogram is 90° show that each of its angle measures 90°

Answer 1

Step-by-step explanation:

Consider ABCD be a parallelogram and measure of angle C is 90°.

Now, since ABCD is a parallelogram, then measure of angle will be equal to measure of angle A, that is

m∠C=m∠A=90° (Opposite angles of parallelogram are equal)

and m∠A+m∠B=180 (Corresponding angles)

⇒90+m∠B=180

⇒m∠B=90

Also, m∠B=m∠D=90°(Opposite angles of parallelogram are equal)

Thus, m∠A=m∠B=m∠C=m∠D=90°.

Since, all the angles of the parallelogram are equal to 90, therefore ABCD is a rectangle, by the properties of rectangle.

Hence proved.

Answer 2

Dear Student,

# Proof -

Consider a parallelogram, ABCD.

Let A be given angle.

∠A = 90°

As we know, opposite angles of parallelogram are equal.

∠C = ∠A

∠C = 90°

Adjacent angles of parallelogram is supplementary.

∠A + ∠B = 180°

90° + ∠B = 180°

∠B = 180° - 90°

∠B = 90°

Also, ∠D is equal to ∠B.

∠D = ∠B

∠D = 90°

Thanks dear. Hope this helps you...