Selina solutions

Grade 6

# Question 12

Q12)

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.

Solution 12:

Two lines AB and CD intersect each other at O

\angle AOC=68°

(i) AOB is a line

\angle AOC+\angle BOC=180°

68° +a=112°

a= 180° - 68° = 112°

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

(iii) \angle AOC\ and\ \angle BOD;\ \angle BOC\ and\ \angle BOD;\ \angle BOD\ and\ \angle DOA are pairs of adjacent angles

(iv) \angle BOC\ and\ \angle DOA\ are reflex angles and also

\angle AOC\ and\ \angle BOD\ are\ also\ reflex\ angles

Ref. \angle BOC= 180° +68° =248°

Ref. \angle DOA= 180° +68° =248°

Ref. \angle AOC= 180° +112° =292°

and red. \angle BOD= 180° +112° =292°

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