The vertical angle theorem states that two opposite vertical angles formed by two lines intersecting each other are always equal (congruent).

Vertical angles theorem. Calculate the unknown angles in the following figure. The given information, what needs. In this example a° and b° are vertical angles.

It’s a line that runs from top to bottom and from bottom to top. 4 rows the vertical angle theorem states that the angles formed by two intersecting lines which are. A full circle is 360°, so that leaves 360° − 2×40° = 280°.

Two lines are intersecting in the above figure. Also, a vertical angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. ∠ 1 and ∠ 2 form a linear pair, so by the supplement postulate, they are supplementary.

Vertical angle examples example 1. Like the rest of these, the vertical angles theorem serves a foundational role in the rules of geometry and trigonometry. We can write the linear pairs of angles equal to 180.

∠ 47 0 and ∠ b are vertical angles. In picture 2, ∠ 1 and ∠ 2 are vertical angles. Vertical angles are the angles formed by the intersection of two lines.

Because b° is vertically opposite 40°, it must also be 40°. Likewise, ∠ a and ∠ b are vertical. Yes, we can solve equations involving angles and linear pairs by using vertical angles theorem or congruency theorem.