Question

The measures of two adjacent angles of a parallelogram are in the ratio 3:2 find the measures of each of the angles of the parallelogram

Answer 1

hiii!!!

here's ur answer...

we know that the sum of two adjacent angle in a parallelogram is 180°.

let the two adjacent Angles be 3x and 2x.

therefore 3x + 2x = 180°

=> 5x = 180°

=> x = 180/5

=> x = 36°

hence, 3x = 3 × 36

= 108°

and 2x = 2 × 36

= 72°

other two Angles are also 108° and 72°, as we know that opposite angles are equal.

VERIFICATION:-

we know that the sum of all angles in a parallelogram is 360°

= 108° + 108° + 72° + 72°

= 216° + 144°

= 360°

hence verified

each angle of the parallelogram are :-

108°, 72°, 108° and 72°

hope this helps u..!

Answer 2

Answer:

Let the measures of two adjacent angles, ∠A and ∠B, of parallelogram ABCD are in the ratio of 3:2.

Let ∠A = 3x and ∠B = 2x

We know that the sum of the measures of adjacent angles is 180º for a parallelogram.

∠A + ∠B = 180º

3x + 2x = 180º

5x = 180º

∠A = ∠C = 3x = 108º (Opposite angles)

∠B = ∠D = 2x = 72º (Opposite angles)

Thus, the measures of the angles of the parallelogram are 108º, 72º, 108º, and 72º.