Question

If a transversal intersects two parallel lines and the ratio between interior angles on the same side of the transversal in 3.7 , then find the measure of the smaller angle​

Answer 1

Given:

• Two interior angles on the same side of a transversal intersecting two parallel lines are in ratio 3 :7

To find:

• What is the smaller angle ?

Solution:

Let ,

• the angles be 3x and 7x

We know that,

• Sum of angles on the same side of transversal intersecting two parallel lines is 180°.

$\\\sf{:\implies 3x + 7x = 180°}$

$\sf{:\implies 10x = 180°}$

$\sf{:\implies x =\dfrac{180°}{10}}$

$\sf{:\implies x = 18°}$

${\bf{\pink{⟹\:\:x\:\:=\:\:18°}}}$

So the angles are:

• 3x = 3 × 18° = 54°

• 7x = 7 × 18° = 126°

Therefore, the smaller angle is 54°