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,
[tex]m\angle 1+m\angle 2=180^\circ[/tex]
[tex]x^\circ+(x+50)^\circ=180^\circ[/tex]
[tex]2x^\circ+50^\circ=180^\circ[/tex]
[tex]2x^\circ=180^\circ-50^\circ[/tex]
[tex]2x^\circ=130^\circ[/tex]
Divide both sides by 2.
[tex]x^\circ=65^\circ[/tex]
[tex]x=65[/tex]
Now,
[tex]m\angle 1=65^\circ[/tex]
[tex]m\angle 2=(65+50)^\circ=115^\circ[/tex]
Therefore, the correct option is C.
