Question

In the given figure, lines AB and CD intersect at point O.
(i) Find the value of ∠a.
(ii) Name all the pairs of vertically opposite angles.
(iii) Name all the pairs of adjacent angles.
(iv) Name all the reflex angles formed and write the measure of each.

Answer 1

Two lines AB and CD intersect each other at O

∠AOC = 68°

(i) ∵ AOB is a line

∠AOC + ∠BOC = 180°

⇒ 68° + a = 180°

⇒ a= 180°-68° = 112°

(ii) ∠AOC and ∠BOD and ∠BOC and ∠AOD are the two pairs of vertically opposite angles.

(iii) ∠AOC and ∠BOC; ∠BOC and ∠BOD; ∠BOD and ∠DOA; ∠DOA and AOC are the pairs of adjacent angles

(iv) ∠BOC and ∠DOA are reflex angles and also ∠AOC and ∠BOD are also reflex angles.

Ref. ∠BOC = 180° + 68° = 248°

Ref. ∠DOA = 180° + 68° = 248°

Ref. ∠AOC = 180° + 112° = 292°

and ref. ∠BOD =180° + 112° = 292°