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

Given: mKP=2mIP, mIVK =120° Find: m∠KJL.-example-1
User Aneesa
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1 Answer

6 votes

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°.

User Yarim
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