Q2 of 23 Page 94

In the given figure, OP bisect ∠ BOC and OQ bisect ∠ AOC. Then ∠ POQ is equal to

Suppose that


BOC = 2x and ∠ AOC = 2y


Now, by question; OP and OQ is the bisect or of ∠ BOC and ∠ AOC respectively.


⇒


Similarly,



Now,


∠ POQ = ∠ POC + ∠ COQ = x + y


So, we have to find ∠ POQ i.e.x + y Now, ∠ BOC + ∠ AOC = 180


⇒ 2x + 2y = 180


⇒ 2(x + y) = 180


⇒ x + y = 180/2


⇒ x + y = 90°


Hence, ∠ POQ = 90°.

More from this chapter

All 23 →
10

In the given figure at right, side BC of ΔABC is produced to D. Find ∠A and ∠C.

 1

If an angle is equal to one third of its supplement, its measure is equal to

 3

The complement of an angle exceeds the angle by 60°. Then the angle is equal to

 4

Find the measure of an angle, if six times of its complement is 12° less than twice of its supplement.