Question

Find the value of x, if m arc FN = 5x – 10 and m= arc UN = 3x + 30.

Answer 1

x=20

Explanation:

we know that

Triangles YNF and YUN are congruent by SSS

Because

YN=YF=YU=r -----> the radius of the circle

FN=NU ----> given problem

therefore

∠FYN=∠NYU

and

arc FN=∠FYN -----> by central angle

arc NU=∠NYU -----> by central angle

so

arc FN=arc NU

substitute the given values

5x-10=3x+30

solve for x

5x-3x=30+10

2x=40

x=20