georgiaarchery
georgiaarchery georgiaarchery
  • 19-10-2018
  • Mathematics
contestada

ΔMNP is an isosceles triangle with MN ≈NP. If ∠ M = 3x + 1 and ∠ N = x - 11. What is the measure of ∠P?
A) 20
B) 27
C) 82
D) 112

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remotecontrolbrain
remotecontrolbrain remotecontrolbrain
  • 19-10-2018

Start with an equation summing all the angles in this triangle:

180 = <M + <N + <P

we are given <M and <N but not <P. But, since MN=NP, the angle <P is the same as the angle <M (isosceles, make a drawing to see). So

180 = 2<M + <N

180 = 2(3x+1) + x-11

180 = 7x - 9

x = 27

<P = 3*27+1 = 82 degrees

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