Solved Examples on Vertically Opposite Angles
Following are some solved examples on Vertically Opposite Angles:
Example 1: If ∠A and ∠B are vertical angles, and the measure of ∠A is 120 degrees, what is the measure of ∠B?
Vertical angles are always congruent, meaning they have the same measure. Therefore, if ∠A measures 120 degrees, ∠B will also have the same measure.
So, the measure of ∠B is 120 degrees.
Example 2: If the sum of the measures of two vertical angles is 120 degrees, what is the measure of each individual angle?
Denote the measures of the two vertical angles as ∠X and ∠Y.
Given that ∠X + ∠Y = 120 degrees.
We need to find the individual measures of ∠X and ∠Y.
Since vertical angles are congruent, ∠X = ∠Y.
Let ∠X = ∠Y = x (for simplicity).
Now, the equation becomes:
x + x = 120
⇒ 2x = 120
⇒ x = 60
So, each angle measures 60 degrees. Therefore, ∠X = 60 degrees and ∠Y = 60 degrees.
Vertically Opposite Angles
Vertically Opposite Angles, also called Vertical Angles; are angles that stand across from each other when two lines intersect. Imagine two straight lines crossing like a giant letter ‘X.’ The angles formed on opposite sides of this intersection are called vertically opposite angles. These angles share a unique relationship – they are equal to each other. So, if you know the measurement of one vertically opposite angle, you automatically know the size of the other.
In this article, we have covered the concept of vertical angles. such as definition, theorem and proof, properties, formation, and applications of vertical angles.
Table of Content
- What are Vertically Opposite Angles?
- Vertically Opposite Angle Theorem
- Formation of Vertically Opposite Angles
- Applications of vertically Opposite Angles
- Solved Examples