Use an algebraic equation to find the measure of each angle that is represented in terms of x.

Solution:

Given, the angles are (11x - 26)°and (7x + 26)°

We have to find the measure of each angle.

When two lines intersect, the opposite (X) angles are equal.

In the diagram above, angles a and c are equal, and angles b and d are equal.

Thus, the angles formed are vertically opposite angles because they are opposite to each other at a vertex.

From the figure, it is obvious that the two angles are vertically opposite angles.

⇒ 11x - 26 = 7x + 26

⇒ 11x - 7x = 26 + 26

⇒ 4x = 52

⇒ x = 13

Thus, the value of x is 13°.

Now substitute the value of x to find the measure of each angle,

LHS = 11x - 26 = 11(13) - 26

= 143 - 26

= 117°

Similarly, RHS = 7x + 26 = 7(13) + 26

= 91 + 26

= 117°

LHS = RHS

Therefore, the measure of each angle is 117°.

Use an algebraic equation to find the measure of each angle that is represented in terms of x.

Summary:

Using an algebraic equation, the measure of each angle that is represented in terms of x is 117°.