Question

the measure of two adjacent angle of parallelogram in the ratio 3:2. Find the measure of each of angles of the parallelogram.​

Answer 1

Answer:

Step-by-step explanation:

GIVEN :-

ratio between two adjacent angles of a parallelogram is = 3 : 2

let the adjacent angles be 3x and 2x respectively.

we know that,

sum of two adjacent angles in a parallelogram = 180°

⇒ 3x + 2x = 180°

⇒ 5x = 180°

⇒ x = 180/5

⇒ x = 36°

therefore the adjacent angles are :-

3x = 3 * 36 = 108°

2x = 2 * 36 = 72°

we also know that the opposite angles of a parallelogram are equal.

therefore the other two adjacent angles are also 108° and 72°

hence, all the angles of the parallelogram are 72°, 108°, 72° and 108°

Answer 2

Let the common ratio be "x"

Let ∠1,2,3,4 be the angles of the parallelogram.

Given: Measure of two adjacent angle of parallelogram in the ratio 3:2

I.e, ∠1 = ∠3 = 3x -------(opposite angles in a lllgm are equal)

∠2 = ∠4 = 2x -------(opposite angles in a lllgm are equal)

We know that, ∠1 + ∠2 + ∠3 + ∠4 = 360⁰

So, 3x + 2x + 3x + 2x = 360⁰

---> 10x = 360⁰

---> x = 360⁰/10

---> x = 36⁰

Now, we just have to find all the angles of the lllgm

∴∠1 = ∠3 = 3x = 3(36⁰) = 108⁰

∴∠2 = ∠4 = 2x = 2(36⁰) = 72⁰

108⁰, 72⁰, 108⁰, 72⁰ are the required angles.