Also, a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees.

Vertical angles are congruent. An example of congruent angles which are not. When two lines intersect to make an x, angles on opposite sides of the x are called vertical angles. Let us check the proof of it.

M ∠ x in digram 1 is 157 ∘ since its vertical angle is 157 ∘. A pair of vertically opposite angles are always equal to each other. Both pairs of vertical angles (4 angles that share the same vertex) always add up to 360°.

According to the vertical angle theorem, two intersecting lines that form vertical angles are congruent. Vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent. Consider the two lines ab and cd intersecting each other at the point o.

In the figure above, ∠dof is bisected by oe so, ∠eof≅∠eod. Likewise, ∠ a and ∠ b are vertical. The vertical angles are of equal measurements.

Vertical angles share the same vertex (the common corner point) but they cannot share a side. Let’s get familiar with the characteristics of vertical angles by delving into a few examples. The vertical angles are formed.

Vertical angles must necessarily be congruent, however congruent angles do not necessarily have to be vertical angles. And thus you can set their measures equal to each other: We have to prove that: