Answer:
The measure of angle KJL is 40°.
Step-by-step explanation:
Givens
[tex]m(KP)=2m(IP)[/tex]
[tex]m(IVK)=120\°[/tex]
Notice that
[tex]m(KP)+m(IP)+m(IVK)=360\°[/tex], by definition sum of arcs.
Replacing given values, we have
[tex]2m(IP)+m(IP)+120\°=360\°\\3m(IP)=360\° - 120\°\\m(IP)=\frac{240\°}{3}\\ m(IP)=80\°[/tex]
Which means [tex]m(KP)=2(80\°)=160\°[/tex]
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.
[tex]m\angle KJL = \frac{1}{2} (m(KP)-m(IP))\\m \angle KJL = \frac{1}{2}(160\° - 80\° )=\frac{1}{2}(80\°)=40\°[/tex]
Therefore, the measure of angle KJL is 40°.
