Given :-
m∠WRM = 5x - 13
m∠KRW = 2x - 5
m∠KRM = 37°
As m∠KRW and m∠KRM are forming m∠WRM , their sum will be equal to the measure of m∠WRM .
Which means :-
[tex]2x - 5 + 37 = 5x - 13[/tex]
[tex] - 5 + 37 = 5x - 13 - 2x[/tex]
[tex] - 5 + 37 = 3x - 13[/tex]
[tex]32 = 3x - 13[/tex]
[tex]3x = 32 + 13[/tex]
[tex]3x = 45[/tex]
[tex]x = \frac{45}{3} [/tex]
[tex]\color{olive}\implies\color{hotpink}x = 15[/tex]
m∠KRW :-
[tex] = 2 \times 15 - 5[/tex]
[tex] = 30 - 5[/tex]
[tex]\color{olive}\implies \: \color{hotpink}m∠KRW= 25°[/tex]
Given :-
[tex]\color{olive}\implies \: \color{hotpink}m∠KRM = 37°[/tex]
m∠WRM :-
[tex] = 5 \times 15 - 13[/tex]
[tex] = 75 - 13[/tex]
[tex]\color{olive}\implies \:\color{hotpink} m∠WRM = 62° [/tex]
As the sum of m∠KRW and m∠KRM add upto the measure of m∠WRM (25 + 37 = 62) we have found out the correct measure of the angles .
Therefore , the measure of :-
[tex]\color{olive}\implies \:\color{hotpink} m∠WRM = 62° [/tex]
