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.
Accepted Solution
A:
Answer:The measures of the intercepts arcs are [tex]58\°[/tex] and [tex]122\°[/tex]Step-by-step explanation:we know thatThe measurement of the outer angle is the semi-difference of the arcs which comprisesLetx,y -----> the intercepts arcs[tex]x+y=180\°[/tex] ----> equation A[tex]32\°=\frac{1}{2}(x-y)[/tex][tex]64\°=(x-y)[/tex][tex]x=64\°+y[/tex] ------> equation Bsubstitute equation B in equation A[tex](64\°+y)+y=180\°[/tex][tex]64\°+2y=180\°[/tex][tex]2y=180\°-64\°[/tex][tex]y=116\°/2=58\°[/tex]Find the value of x[tex]x=64\°+58\°=122\°[/tex]thereforeThe measures of the intercepts arcs are [tex]58\°[/tex] and [tex]122\°[/tex]