Question

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 5:4. Then the greater of the two angles is

Answer 1

✬ Greater angle = 100° ✬

Step-by-step explanation:

Given:

• Ratio of two interior angles on same side of a transversal is 5 : 4.

To Find:

• What is the measure of greater angle ?

Solution: Let x be the common in given ratios. Therefore,

➼ First angle = 5x°

➼ Second angle = 4x°

As we know that sum of interior angles on same side of transversal intersecting two parallel line is 180.

$\implies{\rm }$ (First + Second) angle = 180

$\implies{\rm }$ 5x + 4x = 180

$\implies{\rm }$ 9x = 180

$\implies{\rm }$ x = 180/9

$\implies{\rm }$ x = 20°

So,

➟ First angle = 5x = 5(20) = 100°

➟ Second angle = 4x = 4(20) = 80°

On comparing both these two angles we got

• First angle > Second angle

∴ Hence, the greater of two angles is 100°.

Answer 2

✬ Greater angle = 100° ✬

Step-by-step explanation:

Given:

Ratio of two interior angles on same side of a transversal is 5 : 4.

To Find:

What is the measure of greater angle ?

Solution: Let x be the common in given ratios. Therefore,

➼ First angle = 5x°

➼ Second angle = 4x°

As we know that sum of interior angles on same side of transversal intersecting two parallel line is 180.

⟹ (First + Second) angle = 180

⟹ 5x + 4x = 180

⟹ 9x = 180

⟹ x = 180/9

⟹ x = 20°

So,

➟ First angle = 5x = 5(20) = 100°

➟ Second angle = 4x = 4(20) = 80°

On comparing both these two angles we got

First angle > Second angle

∴ Hence, the greater of two angles is 100°.