Question

Two straight lines intersect each other at O. The measure of two adjacent supplementary angles are given in terms of x. Find the measure of the vertically opposite angles thus formed in degrees.​

Answer 1

Answer:

Given AB and CD are straight lines which intersect at O. OP is the bisector of ∠AO.

To prove: OQ is the bisector of ∠BOD.

Proof: AB, CD and PQ are straight lines which intersect in O.

∠AOP=∠BOQ(vertically opposite angles)

∠COP=∠DOQ(vertically opposite angles)

∠AOP=∠COP(OP is the bisector of ∠AOC)

∴∠BOQ=∠DOQ

Thus, the rate opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle. Similarly, the bisection of ∠AOD also bisects the ∠BOC.

solution

Step-by-step explanation:

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