So in such cases, we can say that vertical angles are supplementary. Therefore, the sum of these two angles will be equal to 180°. If there is a case wherein, the vertical angles are right angles or equal to 90°, then the vertical angles are 90° each. When any two angles sum up to 180°, we call them supplementary angles. Vertical angles are congruent as the two pairs of non- adjacent angles formed by intersecting two lines superimpose on each other. ![]() Vertical angles are always congruent and equal. When two straight lines intersect each other vertical angles are formed. They are also referred to as 'vertically opposite angles. ![]() Out of the 4 angles that are formed, the angles that are opposite to each other are vertical angles. Vertical angles are formed when two lines intersect each other. Let us look at some solved examples to understand this.įAQs on Vertical Angles What are Vertical Angles in Geometry? To find the measure of angles in the figure, we use the straight angle property and vertical angle theorem simultaneously. Therefore, we conclude that vertically opposite angles are always equal. we can use the same set of statements to prove that ∠1 = ∠3. (3)īy eliminating ∠1 on both sides of the equation (3), we get ∠2 = ∠4. Therefore, we can rewrite the statement as ∠1 + ∠2 = ∠1 +∠4. ∠1 +∠4 = 180° (Since they are a linear pair of angles) - (2)įrom equations (1) and (2), ∠1 + ∠2 = 180° = ∠1 +∠4.Īccording to transitive property, if a = b and b = c then a = c. ∠1 + ∠2 = 180° (Since they are a linear pair of angles) - (1) We already know that angles on a straight line add up to 180°. The proof is simple and is based on straight angles. Statement: Vertical angles (the opposite angles that are formed when two lines intersect each other) are congruent. Let's learn about the vertical angles theorem and its proof in detail. Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
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