In the figure above, MQ and NR intersect at point P, NP = QP  , and MP = PR  . What is the measure, in degrees, of ∠QMR ? (Disregard the degree symbol when gridding your answer.)

The correct answer is: 30 degrees

Step by step solution:
In the given figure, it is given that MP = PR
We know that if a triangle has two sides of equal length, it is called an isosceles triangle
Triangle MPR is an isosceles triangle
We know that in an isosceles triangle the two angles opposite to the equal sides are congruent to each other i.e. they are equal
 and  ware equal
Let    =  =  x                   ---- (1)
Now, we can see that  = 180°       ( straight angle)

    ( in figure ÐRPQ = 60°)

Now, we know that sum of all the angles of a triangle is  180°
          ( from (1) )
We can see that  = 30°
Hence, answer = 30°