In the figure above, if MP bisects ∠NMR, then x =

Question

https://gmatclub.com/forum/download/file.php?id=54378 In the figure above, if MP bisects ∠NMR, then x = (A) 80 (B) 90 (C) 100 (D) 110 (E) 120 1.jpg

GMATinsight · Answer

Angle NMR = 180 - (40+80) = 60

Angle PMR = (1/3)*60 = 30

Now, in triangle PMR, 30+x+40 = 180

i.e. x = 110

Answer: Option D

Kinshook · Answer

Asked: In the figure above, if MP bisects ∠NMR, then x =

∠NMR = 180 - (80+40) = 60

∠RMP = 60/2 = 30

x = ∠MPR = 180 - (40 + 30) = 110

IMO D

lacktutor · Answer

Let  y  be the angle of < NMR
 \frac{y}{2 }+ x + 40 = 180  
 \frac{y}{2 }+ 180 —x + 80 = 180

\frac{y}{2 }+ x = 140 
 x —\frac{ y}{2 }= 80 
—>  2x = 220  
—>  x = 110

Answer ( D)

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BrentGMATPrepNow · Answer

Let's first focus on the red triangle below.
Since angles in a triangle must add to 180°, we know that the missing angle must be   60°  
 https://i.imgur.com/GyyeRlI.png

Next, since we're told that MP bisects ∠NMR, we know that each angle must be   30°  
 https://i.imgur.com/9G0ZSSm.png

Finally, we'll focus on the red triangle below.
 https://i.imgur.com/ExSMMGC.png 
Since angles in a triangle must add to 180°, we can write:  x +    30    + 40 = 180

Solve, to get: x = 110

Answer: D

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In the figure above, if MP bisects ∠NMR, then x =

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