In geometry, pairs of angles can relate to each other in several ways.
In this lesson, we will learn
Related Topics: More Geometry Lessons
When two lines intersect, the opposite angles form vertical angles or vertically opposite angles. They are called vertical angles because they share the same vertex.
The Vertical Angle Theorem states that
Vertical angles are equal.
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 are supplementary angles i.e. their sum is 180°. Similarly, s and r are supplementary angles.
The following diagram shows another example of vertical angles.
The following video explains more about vertical angles.
How to define and identify vertical angles
A group of examples that identifies vertical angles
Very often math questions will require you to work out the values of angles given in diagrams by applying the relationships between the pairs of angles.
Given the diagram below, determine the values of the angles x, y and z.
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°
Both AEC and DEB are straight lines. Find q.
← vertical angles
q + 45˚= 135˚
q = 135˚ – 45˚ = 90˚
The following video shows how to use the vertical angle theorem to solve problems.
Identify vertical angles and find the missing angle measures from a diagram.
The following video shows how to find a missing vertical angle in a triangle.
The following videos will prove that vertical angles are equal.
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