Question

If P is the incenter of triangle JKL, find m? What would be the measure for m :D​

Answer 1

Answer:

∠JKP = 35°

Step-by-step explanation:

Given P is the incentre of the triangle,

ie., P is the point of intersection of all 3 angular bisectors.

so, from vertex J we have the angular bisector JN dividing the ∠J such that ∠KJN = ∠NJL

ie, (7x-6) = 5x+4

=> 7x-5x = 4+6

=> 2x = 10

=> x= 10/2 = 5

so, the angles are ∠KJN = 7(5)-6 = 35-6 = 29°

and ∠NJL = 5(5)+4 = 25+4 = 29°

adjacent to the vertex J, we have L with angular Bisector LM dividing the ∠L such that ∠KLM = ∠MLJ

so, given that ∠KLM = 26° => ∠MLJ = 26°

so, we have ∠J = 29°+29° = 58°

and ∠L = 26°+26° = 52°

In the given ΔJKL, we know ∠J + ∠K + ∠L = 180°

=> 58°+ ∠K + 52° = 180°

=> ∠K + 110° = 180°

=> ∠K = 180° - 110°

=> ∠K = 70°

we have angular bisector, KO bisecting ∠K such that ∠JKO = ∠OKL

we know, ∠K = ∠JKO +∠OKL

also, 70° = ∠JKO +∠JKO ( as angular bisectors)

70° = 2∠JKO

=> ∠JKO = 70°/2 = 35°

from the diagram, ∠JKO = ∠JKP

and hence ∠JKP = 35°