Question

Two lines l and m intersect at a point O. If anglex = 100°, the measure of angles angle 1, angle 2 and angle three
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Answer 1

Lines, l and m and n intersect at point O,P is a point on line n and such that P is equidistant from l and n.

Refer image,

To prove: n us the bisector of ∠QOR

Proof: In ΔOQP and ΔORP, we have

∠1=∠2

[∵ Each equal to 90° ]

OP=OP [Common side]

PQ=QR [Given]

So, by RHS criterion of congruence, we have

ΔOQP≅ΔORP

∴∠3=∠4 [CPCT]

So, n is bisector of ∠QOR

Hence, proved.