Question

In the figure line l is parallel to line m , line p is the transversal if r = 20° then find a: b

Answer 1

Step-by-step explanation:

Given: Figure

To find: a:b

Solution:

It is given that $\angle r=20°$

We know that $\angle a$ and $\angle r$ are Vertically opposite angles,thus

$\angle a= \angle r$

Thus,

$\bold{\red{\angle a=20°}}$

Now,

$\angle a$ and $\angle b$ are consecutive interior angles.

Thus,

$\angle a+\angle b=180°$

$20°+\angle b=180°$

$\bold{\green{\angle b=160°}}$

So,

Ratio of both angles

$\frac{\angle a}{\angle b} = \frac{20}{160} \\ \\ \frac{\angle a}{\angle b} = \frac{1}{8}$

Final answer:

a:b= 1:8

Hope it helps you.