Question

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram?

Answer 1

$<marquee direction="right"><big>Hi friend!</big></marquee>$

$<b><u><big><big>Answer:</big></big></u></b>$

We know that, in a parallelogram ABCD:

Angle A = Angle C, Angle B = Angle D
Angle A + Angle B = 180° = Angle C + Angle D
and
Angle A + Angle B + Angle C + Angle D = 360°
$<hr size=2 color="grey">$
Given that:
Adjacent angles are equal.
"Angle A = Angle B"

As opposite angles are equal,
Angle A = Angle C, Angle B = Angle D

Since Angle A = Angle B,
Angle A = Angle B = Angle C = Angle D
and
Angle A + Angle B + Angle C + Angle D = 360°

Now that we have got so many clues, let's try to find the answer!
$<hr size=5 color="green">$
Let Angle A be 'x'

Since all angles are equal,
$x + x + x + x = 360° \\ 4x = 360° \\ x = \frac{360°}{4} \\ x = 90°$

Angle A = Angle B = Angle C = Angle D = x = 90°

$Therefore, each of the angles equal to <b>90°</b>.$

Hope you found my answer helpful. Keep Smiling!

Answer 2

Answer:

Let the parallelogram be ◻ABCD.

Sum of adjacent angles = 180 ∘

∠A + ∠B = 180 ∘

2∠A = 180 ∘ (Given ∠A = ∠B)

∠A = 90 ∘

∠A = ∠B = 90 ∘

∠B = ∠D = 90 ∘

All angles are equal to 90 ∘