Question

Given mZ1= x° and m Z2 = (x +50)".

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.