This theorem says that when two straight lines intersect,.

Vertical angles are congruent. Whenever an angle is bisected, two congruent angles are formed. An example of congruent angles which are not. M ∠ x in digram 1 is 157 ∘ since its vertical angle is 157 ∘.

Like the rest of these, the vertical angles theorem serves a foundational role in the rules of geometry and trigonometry. These angles are equal, and here’s the official theorem that tells you. 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 are angles in opposite corners of intersecting lines. A pair of vertically opposite angles are always equal to each other.

Vertical angles must necessarily be congruent, however congruent angles do not necessarily have to be vertical angles. The vertical angles are of equal measurements. M ∠ 1 ≅ m ∠ 3.

Notice how the 4 angles are actually two pairs of vertical angles: Vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent. In picture 2, ∠ 1 and ∠ 2 are vertical angles.

The vertical angles are of equal measurements. Likewise, ∠ a and ∠ b are vertical. Vertical angles share the same vertex (the common corner point) but they cannot share a side.