Question

In the image m || n || p.

Given ∠10 = 2x + 70

∠7 = 5x – 20



Find m∠3.

Answer 1

Given:

In the given figure
`m\parallel n\parallel p`.

`m\angle 10=2x+70`

`m\angle 7=5x-20`

To find:

The
`m\angle 3`.

Solution:

If a transversal line intersect two parallel lines, then the alternate exterior angles are equal.

`m\angle 7=m\angle 10` (Alternate exterior angle)

`2x+70=5x-20`

`70+20=5x-2x`

`90=3x`

Divide both sides by 3.

`(90)/(3)=(3x)/(3)`

`30=x`

Now,

`m\angle 3=m\angle 7` (Corresponding angles)

`m\angle 3=5x-20`

`m\angle 3=5(30)-20`

`m\angle 3=150-20`

`m\angle 3=130`

Therefore, the measure of angle 3 is 130 degrees.