Question

if two interior angles on the same side of the transversal intersecting two parallel lines are in the ratio 2:3 then find the greater of the two angles​

Answer 1

it means that angles are in ratio of 2 and 3 ,sum of the ratio=3+2=5, so greater angle = 3/5 of 180(degrees)= 108(degrees)

Answer 2

Let the angles be 2M and 3M.

Here..

• 2M = smaller angle
• 3M = larger angle

Two interior angles on the same side of the traversal intersecting two parallel lines.

Now,

Sum of interior angles is 180°.

⇒ 2M + 3M = 180°

⇒ 5M = 180°

⇒ M = 180°/5

⇒ M = 36

Now, substitute value of M in assumed angles to find their value.

So,

$\therefore \:\sf{Smaller\:angle\:2M}$

⇒ 2(36°)

⇒ 72°

$\therefore \:\sf{Larger\:angle\:3M}$

⇒ 3(36°)

⇒ 108°

•°• 108° is the greater angle of the two angles.