Question

Given mZ1= x° and m Z2 = (x +50)".

Find the value of x. Then find m21 and 22.
x = 20; mZ1= 20 and 22 - 70
x = 20; m_1 = 65 and m_2 = 115
x = 65; m_1 = 65 and m2 = 115
x = 65; m_1= 20 and m_2 = 70

Answer 1

Given:

m∠1= x° and m∠2 = (x +50)°.

To find:

The value of x, m∠1 and m∠2.

Solution:

From the figure it is clear that, transversal side intersect the opposite sides which are parallel and form ∠1 and ∠2.

Sum of same sided interior angles is 180 degrees. So,

`m\angle 1+m\angle 2=180^\circ`

`x^\circ+(x+50)^\circ=180^\circ`

`2x^\circ+50^\circ=180^\circ`

`2x^\circ=180^\circ-50^\circ`

`2x^\circ=130^\circ`

Divide both sides by 2.

`x^\circ=65^\circ`

`x=65`

Now,

`m\angle 1=65^\circ`

`m\angle 2=(65+50)^\circ=115^\circ`

Therefore, the correct option is C.