Question

If a transversal intersects two parallel lines such that the interior angles formed on the same side of the transversal is 3x° and 7x°, then the measure of the smaller angle is _

Answer 1

Answer :-

• Smaller angle is 54°

Given :-

• A transversal intersects two parallel lines such that the interior angles formed on the same side of the transversal is 3x° and 7x°.

To Find :-

• Measure of the smaller angle.

Solution :-

As we know that

Angles formed by a transversal line with two parallel lines, interior angles are supplementary.

According to question :-

⇒ 3x + 7x = 180 [ sum of supplementary angles is 180° ]

⇒ 10x = 180

⇒ x = 180/10

⇒ x = 18

Put the value of x in the ratio

• First angle = 3x = 3 × 18 = 54°
• Second angle = 7x = 7 × 18 = 126°

→ 54 < 126

Hence, the smaller angle is 54°.