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

6 answers
Question:

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

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


Answers

The measurement of arc KL is [tex]8\°[/tex]

Step-by-step explanation:

Let

x--------> the measure of arc KL

y-------> the measure of arc MJ

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

[tex]m<MEJ=\frac{1}{2}(y-x)[/tex]

we have

[tex]m<MEJ=16\°\\ y=5x[/tex]

substitute the given value

[tex]16\°=\frac{1}{2}(5x-x)\\ 32\°=(4x)\\ x=8\°[/tex]

therefore

The measurement of arc KL is [tex]8\°[/tex]

∠1=38°

Step-by-step explanation:

KM bisects ∠JML. Therefore, ∠JMN=∠LMN

∠JMN=∠LMN

38°=∠1

∠JML = 76°

Step-by-step explanation:

since it is a kite, ∠1 = 38°

∠JML = 2(38°) = 76°

Angle KLM = 86 hope that helps

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