Question

AP and CP are bisectors of a and c respectively and l parallel to M find the measure of angle APC

Answer 1

∠APC = 90°

Step-by-step explanation:

Given:

Here AP and CP are the bisectors of A and C respectively and also L parallel to M.

∠LAC + ∠ACM = 180°   [co interior angles]

Dividing both the sides by 2, we get

$\frac{\angle LAC}{2}+\frac{\angle ACM}{2} =\frac{180}{2}$

∠LAC + ∠ACP = 90°         [Given]          [1]

Now, in Δ ACP

∠PAC + ∠ACP + ∠APC = 180°   [Angle sum property]

90° + ∠APC = 180°

∠APC = 180° - 90°

∠APC = 90°

Answer 2

Answer:

90

Step-by-step explanation:

Given:

Here AP and CP are the bisectors of A and C respectively and also L parallel to M.

∠LAC + ∠ACM = 180° [co interior angles]

Dividing both the sides by 2, we get

\frac{\angle LAC}{2}+\frac{\angle ACM}{2} =\frac{180}{2}

2

∠LAC

+

2

∠ACM

=

2

180

∠LAC + ∠ACP = 90° [Given] [1]

Now, in Δ ACP

∠PAC + ∠ACP + ∠APC = 180° [Angle sum property]

90° + ∠APC = 180°

∠APC = 180° - 90°

∠APC = 90°