Question

10 - 15

Answer 1

Answer:

JK = 27

NJ = 153

JL = 117

KNM= 207

MJL =297

JLK =333

Step-by-step 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

Answer 2

Answer:

Step-by-step 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