Question

Given: mKP=2mIP, mIVK =120° Find: m∠KJL.

Answer 1

Answer:

The measure of angle KJL is 40°.

Step-by-step 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

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

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.

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

Therefore, the measure of angle KJL is 40°.