Question

Ray OA,OB,OC are three rays in order that
angle AOB = 54, angle BOC 24, OP bisects angle AOC
Find angle POB

Answer 1

Answer:

42 correct or not say if wrong

Step-by-step explanation:

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Answer 2

Given:

Angle AOB=54°

Angle BOC=24°

To find:

Angle POB

Solution:

The measure of angle POB is 15°.

We can find the angle by following the given steps-

We know that the rays OA, OB, and OC form multiple angles.

The angle formed between OA and OB=54°

The angle formed between OB and OC=24°

So, the angle AOC=angle AOB+angle BOC

On putting the values, we get

Angle AOC=54°+24°

Angle AOC=78°

Now, we know that the ray OP bisects the angle AOC.

So, on bisection, angle AOP and angle POC are equal.

Angle AOP=Angle POC=1/2 of angle AOC

Angle AOP=Angle POC=1/2×78°

Angle AOP=Angle POC=39°

We know that the angle POC is the sum of angle POB and angle BOC

Angle POC=angle POB+angle BOC

Using the values,

39°=Angle POB+24°

39°-24°=Angle POB

15°=Angle POB

Therefore, the measure of angle POB is 15°.