Question

If AP and BP are bisectors of angles ∠CAB and ∠CBD respectively, find the angle ∠APB.

Answer 1

Given:

AP and BP are the bisectors of ∠CAB and ∠CBD.

To Find:

Measure of angle APB.

Solution:

Let m∠CAB = 2x°

Therefore, m∠CAP = m∠PAB = x°

Let m∠CBD = 2y°

Therefore, m∠CBP = m∠DBP = y°

Since, ∠CBD is an exterior angle of ΔABC

Therefore, m∠CBD = m∠BAC + m∠ACB

2y° = 2x° + 90°

y° = x° + 45°

y° - x° = 45° -----(1)

Similarly, ∠PBD is an exterior angles of ΔAPB,

m∠PBD = m∠BAP + m∠APB

y = x + m∠APB

m∠APB = y - x

From equation (1),

m∠APB = 45°