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.

$\dfrac{90}{3}=\dfrac{3x}{3}$

$30=x$

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.