Vertical Angles or Vertical Opposite Angles : Solved Examples

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

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" Two line p and q intersect at point "O" and forms ∠ 1, ∠ 2, ∠ 3 and ∠ 4; as shown in the following diagram: Now from the diagram you can see that: (∠ 1 & ∠ 2) and (∠ 3 and ∠ 4) are vertically opposite angles. ∠ 3 and ∠ 4 are of 45° each and so they are acute angles..................Statement (1) Now we have we have to calculate the measure of ∠ 1 and ∠ 2 and it proceeds as: ∠ 3 and ∠ 1 forms a linear pair, so: ∠ 3 + ∠ 1 = 180° ∠ 3 = 45°(see statement 1), so 45° + ∠ 1 = 180° Subtract 45° from both sides and we get: ∠ 1 = 135° Since ∠ 1 and ∠ 2 are vertically opposite angles, so we get: ∠ 1 = ∠ 2 (because vertically opposite angles are equal) ∠ 1 = 135° (solved above), so ∠ 2 = 135° Since, ∠ 1 and ∠ 2 = 135° and so they are obtuse angles .....Statement (2) Hence From Statement (1) and (2), its proved that: "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". Related Question 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"