Question

PLS HELP IN NEXT 10 MINUTES - CLASS IN 20 MINS & WE HAVE A TEST :(((

The vertex of an angle measuring 32° is in the exterior of a circle and its sides are secants of the circle. If the sum of the measures of the intercepted arcs is 180°, find the measure of each intercepted arc.

Answer 1

Answer: Let x = the measure of the larger arc and

let y = the measure of the smaller arc which is closest to the angle’s vertex. We know that x + y = 180 because that is given.

The secant-secant angle has a measure that is half the difference of the intercepts arcs. That means (1/2)(x - y) = 32 for this problem

We just need to solve the system

x + y = 180 and x - y = 64

Adding the equations you get 2x = 244 so x = 122 degrees and y = 58 degrees

Explanation: