Question

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3, then find the greater angle in degree.​

Answer 1

Given :

• Two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3.

To find :

• The greater angle in degree =?

Step-by-step explanation :

It is Given that,

Two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3.

Now,

Let the first interior angle be, 2x.

Then, the second interior angle be, 3x.

As We know that,

Sum of interior angles on same side of transversal intersecting two parallel line is 180°.

Substituting the values, we get,

2x + 3x = 180°

5x = 180°

x = 180°/5

x = 36°

Therefore, We got the value of, x = 36°.

Hence,

The first interior angle, 2x = 2 × 36° = 72°

And Second interior angle, 3x = 3 × 36° = 108°

Hence, greater angle is 108°.

Answer 2

✵ Given ✵

Two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3.

✵ To Find ✵

The greater angle in degree.​

✵ Solution ✵

Let the angles be 2x and 3x.

We know that,

☛ The interior angles on same side of transversal intersecting two parallel line are supplementary (180°).

Now, we get :-

2x + 3x = 180

⇒ 5x = 180

⇒ x = 180/5

⇒ x = 36

_______________

Now, obviously 3x > 2x. So,

3x = 3 × 36

⇒3x = 108°

Therefore, the greater angle measures 108°.