From the given figure 5.15

i. Find the measure of ∠BOD.

ii. Find the measure of ∠AOD.

iii. Which are the pairs of vertically opposite angles?

iv. Which are supplementary angles adjacent to ∠AOC? State.

Given:

∠ AOC = 52°

AB and CD are straight lines

Theory:

Vertically opposite angles are equal

Straight line possesses angle of 180°

(i) As AB and CD are straight lines

∠ AOC and ∠ BOD are vertically opposite angles

∴ ∠ AOC = ∠ BOD

∠ BOD = 52°

(ii) As CD is a straight line

Angle made by it is 180°

∠ AOC + ∠ AOD = 180°

52° + ∠ AOD = 180°

∠ AOD = 180° - 52° = 128°

(iii) As AB and CD are straight lines and O is intersecting point

∠ AOC and ∠ BOD are vertically opposite angles

∠ AOD and ∠ BOC are vertically opposite angles

(iv) As CD is a straight line

∠ AOC + ∠ AOD = 180°

∠ AOD is supplementary angle adjacent to ∠ AOC

As AB is a straight line

∠ AOC + ∠ COB = 180°

∠ COB is supplementary angle adjacent to ∠ AOC