Question

AB is parallel to CD. Determine the value of x.

Answer 1

Given:

Given that the line AB is parallel to CD.

The measure of ∠ABO is 50°

The measure of ∠CDO is 30°

We need to determine the value of x.

Value of x:

Let us draw a line through O, parallel to both AB and CD.

By alternate interior angles, we have;

$\angle 1= \angle ABO$

$\angle 1=50^{\circ}$

and also, we have;

$\angle 2=\angle CDO$

$\angle 2=30^{\circ}$

Thus, the measure of ∠BOC = ∠1 + ∠2

Substituting the values, we have;

$\angle BOC=50^{\circ}+30^{\circ}$

$\angle BOC=x=80^{\circ}$

Thus, the value of x is 80°