Vertical Angles or Vertical Opposite Angles

Right Angle	Acute Angle	Obtuse Angle	Zero Angle	Straight Angle
Complementary Angles	Supplementary angles	Adjacent Angles	Vertical / Vertical Opposite Angles	Linear Pair

When two lines intersect each other, we get Vertical Angles Vertical Angles are also known as Vertically Opposite Angles Below Figure represents Vertical Angles. In the above figure, Lines AC and BD intersect each other at point "O" Therefore, we have two pairs of Vertical Angles or Vertically Opposite Angles ∠ AOD and ∠ BOC, ∠ AOB and ∠ COD Also, vertically opposite angles are equal to each other. So, ∠ AOD = ∠ BOC ∠ AOB = ∠ COD "Vertically Opposite angles are equal to each other", this is proved in the following ways: In the given diagram: ∠ AOB and ∠ BOC forms a linear pair, so ∠ AOB + ∠ BOC = 180° or ∠ BOC = 180° - ∠ AOB..............Statement (1) Also, ∠ AOB and ∠ AOD forms a linear pair, so ∠ AOB + ∠ AOD = 180° or ∠ AOD = 180° - ∠ AOB..............Statement (2) Now in statement (1) and (2), we can see that R.H.S. of both the statements is equal. So, L.H.S. of both the statements would also be equal and we get: ∠ AOD = ∠ BOC And since we know that ∠ AOD and ∠ BOC are vertically opposite angles Hence it's proved that: "Vertically Opposite angles are equal to each other" Study More Solved Questions / Examples Write all the vertically opposite angles in following diagram: Two lines p and q intersect at point “o”. Name all the vertically opposite angles thus formed with the help of a diagram. In the following diagram, write vertically opposite angle of ∠ AOD & ∠ DOC. In the following diagram, ∠ 1 = 30° and ∠ 2 =150°. Find the measure of ∠ 3 and ∠ 4 Prove with diagram, "If two lines intersect at one point and if one pair of vertically opposite angles is acute angles, then the other pair of vertically opposite angles must be obtuse angles"