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

Explanation:

∠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

solution

Answer 2

We know that ,

Opposite Sides of parallelogram are parallel.

So, the adjecent angle will be interior angles of the transversal. . . . which has the sum 180°.

So, let 3x and 2x be the angles . . .

➜ 3x + 2x = 180°

➜ 5x = 180°

➜ x = 36°

So, the angles are . . .  

3x = 36 × 3 = 108°

2x = 2 × 36 = 72°

Now ,

We know ,

opposite angles of parallelogram are equal. . .

So, the angles of parallelogram are 108°,72°,108°,72°.