Vertical Angles

In geometry, pairs of angles can relate to each other in several ways. In this lesson we will explain vertical amgles.

Vertical Angles

When two lines intersect, the opposite angles form vertical angles or vertically opposite angles. Vertical angles are equal. They are called vertical angles because they share the same vertex.

Example:

This means that:
 (i)  q and s are vertical angles
 (ii) q = s

Similarly, p is opposite to r
This means that:
 (i)  p and r are vertical angles
 (ii) p = r

Notice also that p and q supplementary angles i.e. their sum is 180°. Similarly, s and r are supplementary angles.

The following diagram shows another example of vertical angles.

Example:

Given the diagram below, determine the values of the angles x, y and z.

Solution:

Step 1: x is a supplement of 65°.

            Therefore, x + 65° =180° ⇒ x = 180° – 65° = 115°

Step 2: z and 115° are vertical angles.

            Therefore, z = 115°

Step 3: y and 65° are vertical angles.

            Therefore, y = 65°

Answer: x = 115°, y = 65° and z = 115°

Example:
Both AEC and DEB are straight lines.  Find q.

Solution:

   ← vertical angles
 q + 45˚= 135˚
    q = 135˚ – 45˚ = 90˚

The following video explains more about vertical angles.

How to define and identify vertical angles

Proof that vertical angles are equal

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