Ray OQ bisects ∠𝑃𝑂𝑅. Find 𝑚∠𝑃𝑂𝑅 if 𝑚∠𝑃𝑂𝑄 = 24°.

The correct answer is: 48 digres

• Hint:
• Angle bisector bisects the angle in two equal parts.
• If the measure of angle is 2x^o then the angle bisector will bisect it in two parts measuring x^o each.
• Step by step explanation: 
• Given: 

Ray OQ bisects ∠𝑃𝑂𝑅
𝑚∠POQ = 24°

• Step 1:
• Let 𝑚∠POQ = x^o
• As we know angle bisectors bisects the angle in two equal parts.

Hence,
𝑚∠POQ = 𝑚∠QOR = x^o

• Step 2:

From figure it is clear that:
∠POQ + ∠QOR = ∠POR
x + x = ∠POR
2x = ∠POR
We know that x = 24^o
∴ ∠POR = 2x = 2(24)
∠POR = 48^o.

• Final Answer: 

Hence, 𝑚∠𝑃𝑂𝑅 is 48^o.