Question

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:

The measures of the intercepts arcs are $58\°$  and $122\°$

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs which comprises

Let

x,y -----> the intercepts arcs

$x+y=180\°$ ----> equation A

$32\°=\frac{1}{2}(x-y)$

$64\°=(x-y)$

$x=64\°+y$ ------> equation B

substitute equation B in equation A

$(64\°+y)+y=180\°$

$64\°+2y=180\°$

$2y=180\°-64\°$

$y=116\°/2=58\°$

Find the value of x

$x=64\°+58\°=122\°$

therefore

The measures of the intercepts arcs are $58\°$  and $122\°$