Question

The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.​

Answer 1

Answer:

ANSWER

Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

∠A+∠B=180

o

⇒3x+2x=180

o

⇒5x=180

o

⇒x=

5

180

o

=36

o

∴∠3×36

o

=108

o

and, ∠B=2×36

o

=72

o

Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108

o

and ∠D=∠B=72

o

Hence, ∠A=108

o

,∠B=72

o

,∠C=108

o

and ∠D=72

o

Answer 2

Answer:

First of the adjacent angles is 108°

And the second of the adjacent angles is 72°

Step-by-step explanation:

The measure of two adjacent angles of a parallelogram are in the ratio 3:2.

One angle is equal to the exterior of the other adjacent angle.

∴ Adjacent Angles add up to 180°

We know that for a strength of N at a ratio of a:b,

The first part is N x $\frac{a}{a+b}$

And the second part is N x $\frac{b}{a+b}$

∴ First of the adjacent angles is 180° x $\frac{3}{3+2}$ = 108°

And the second of the adjacent angles is 180° x $\frac{2}{3+2}$ = 72°