Question

What is the value of x in this figure?

Answer 1

x = 48°

Explanation:

The value of x is equal to the opposite angle formed by the intersection of two lines known as the Vertical Angles theorem.

Vertical angles

Vertical angles are angles that are non-adjcent, formed by the intersection of two lines. Vertical angles are congruent and we can prove it.

Looking at the picture, let the angle to the right of the 48° angle be y, and the angle opposite be z.

Using the Line theorem, we know that the sum of angles on a line is 180°.

So:

• 48° + y° = 180°
• y° = 132°

Similarly:

• 48° + z° = 180°
• z = 132°

Therefore y° = z°, by the vertical angles theorem.

We can say the same for x and 48°

∴ x = 48° by the Vertical Angles Theorem.

Answer 2

48°

Explanation:

Vertical angles are formed by opposite angles created by intersecting lines

The angles shown are vertical angles.

Vertical angles are congruent ( equal to each other )

This means that x would have a measure of 48 degrees as the angle opposite of it has a measure of 48 degrees