Question

In: Math

in the figure shown, MN and NR intersect at point p. NP=QP, and MP=PR. what is the measure, in degrees of angle QMR?

in the figure shown, MN and NR intersect at point p. NP=QP, and MP=PR. what is the measure, in degrees of angle QMR?

Solutions

Expert Solution

 

From the figure shown, angle NPQ can be obtain by subtracting 60 from 180. This is because, angle NPQ and RPQ are angles on a straight line which add upto 180 degrees. 

angle NPQ =120 degrees.

Angles NPQ and  MPR are equal since they are vertically opposite angles

triangle MPR is an isosceles triangle with one angle being 120 degrees.

to find angle QMR, we subtract 120 from 180 and divide the answer by two

angle QMR = (180-120)/2

            =30 degrees.


The value of angle QMR IS 30 degrees

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