Question

10 - 15

If mZMPL = 63, find each measure.
A)JK =
B)mNJ=
c)mJL=
D)mKNM=
E)mMJL=
F)mJLK=
Note please help me My sleep schedule is ruined from this homework and I got more help me

Answer 1

Explanation:

∠NPK = 180° {straight line}

∠NPM + ∠MPL + ∠LPK = 180°

∠NPM + 63 +90 = 180

∠NPM + 153 = 180

∠NPM = 180 - 153

∠NPM = 27°

∠JPK = ∠NPM {Vertically opposite angles}

∠JPK = 27°

∠NPK = 180° {Straight line angle}

∠NPJ + ∠JPK = 180

∠NPJ + 27 = 180

∠NPJ = 180 - 27

∠NPJ = 153

Answer 2

JK = 27

NJ = 153

JL = 117

KNM= 207

MJL =297

JLK =333

Explanation:

If MPL = 63

We can find MPN

NPK = 180 since it is a straight line

NPK = NPM + MPL + LPK

NPM + MPL + LPK = 180

NPM + 63 + 90 = 180

Combine like terms

NPM +153 = 180

NPM = 27

JPK and NPM are vertical angles so they are equal

JPK = 27

JK has the same measure as the central angle JPK = 27

JK = 27

NPK = 180 since it is a straight line

NPJ + JPK = 180

NPJ + 27 = 180

NPJ = 180-27

NPJ = 153 so NJ = 153

JL = JK + KL = 27+ 90 = 117

KNM=KPN + NPM = 180+ 27 = 207

MJL = MPJ +JPL + KPL= 180+117=297

JLK = 360 -JK= 360 -27=333