Question

P is the incenter of △JKL. Find m∠JKP.
& can you please explain

Answer 1

• m∠MKP = 35°

Explanation:

Incenter is the intersection of angle bisectors.

• ∠MJP = ∠OJP, ∠MKP = ∠NKP, ∠NLP = ∠OLP

First find the value of x:

• 7x - 6 = 5x + 4
• 7x - 5x = 4 + 6
• 2x = 10
• x = 5

Find the angle MJP:

• 7*5 - 6 = 29°

We know sum of interior angles of a triangle is 180°. Using this find the missing angle measure:

• 2*m∠MJP + 2*m∠NJP + 2*m∠MKP = 180°
• m∠MJP + m∠NJP + m∠MKP = 90°
• 29° + 26° + m∠MKP = 90°
• m∠MKP = 90° - 55°
• m∠MKP = 35°