# in the diagram which angles are vertical angles?

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## What are Vertical Angles?

Vertical angles are pair angles formed when two lines intersect. Vertical angles are sometimes referred to as vertically opposite angles because the angles are opposite to each other.

Real-life settings where vertical angles are used include; railroad crossing sign, letter “X’’, open scissors pliers etc. The Egyptians used to draw two intersecting lines and always measure the vertical angles to confirm that both of them are equal.

Vertical angles are always equal to one another. In general, we can say that, 2 pairs of vertical angles are formed when two lines intersect. See the diagram below. In the diagram above:

• ∠a and ∠b are vertical opposite angles. The two angles are also equal i.e. ∠a = ∠
• ∠c and ∠d make another pair of vertical angles and they are equal too.
• We can also say that the two vertical angles share a common vertex (the common endpoint of two or more lines or rays).

## In which diagram are angles 1 and 2 vertical angles? Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines.

## Answer: The angles shown in the first figure (a) are vertical angles.

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Let us understand how to identify vertical angles which are also known as vertically opposite angles.

Explanation:

When two lines intersect, the angles formed opposite to each other are termed as vertical angles.

(a) In the first figure, ∠1 and ∠2 are not adjacent angles. So, ∠1 and ∠2 are vertical angles.

(b) In the second figure, ∠1 and ∠2 are adjacent angles. So, ∠1 and ∠2 are not vertical angles.

### So, the pair of angles in the first figure (a) are vertical angles.

Example:

Determine the value of θ in the diagram shown below. Solution

From the diagram above, ∠ (θ + 20) and ∠ x are vertical angles. Therefore,

∠ (θ + 20)= ∠ x

But 110+ x = 180(supplementary angles)

x = (180 – 110)

= 70