1 Answer

Yarim · Answer 1 · 2021-09-08T01:09:10+0000

Answer:

The measure of angle KJL is 40°.

Explanation:

Givens

m(KP)=2m(IP)

$m(IVK)=120\°$

Notice that

$m(KP)+m(IP)+m(IVK)=360\°$ , by definition sum of arcs.

Replacing given values, we have

$2m(IP)+m(IP)+120\°=360\°\\3m(IP)=360\° - 120\°\\m(IP)=(240\°)/(3)\\ m(IP)=80\°$

Which means
$m(KP)=2(80\°)=160\°$

Notice that arc KP is the subtended arc by angle KJL.

We know that the angle formed by a tangen and a secant is equal to one-half of the difference of the intercepted arcs.

$m\angle KJL = (1)/(2) (m(KP)-m(IP))\\m \angle KJL = (1)/(2)(160\° - 80\° )=(1)/(2)(80\°)=40\°$

Therefore, the measure of angle KJL is 40°.