Question

Find the value of x in the figure below. Show all steps. circle with two secants forming an angle to one side of the circle; the two secants cut out arcs of measure 158 degrees and 64 degrees; the angle formed by the two secants is 9 x minus 5 degrees

Answer 1

the complete question in the attached figure

we know that
An exterior angle is one that has its vertex at an outer point of the circumference.
The measure of the external angle is the semi-difference of the arcs that it covers.

in this problem the external angle is ∡(9x-5)°
and
the semi-difference of the arcs that it covers is (1/2)*(158°-64°)=47°

then
(9x-5)=47-------> 9x=47+5----------> 9x=52--------> x=5.78°

the answer is
x=5.78°