Question

The figure shows secants LH and LI and tangent JK intersecting at point L. HIL is a right triangle. Find the measure of KLI and the measure of LI.
A. KLI=32
LI=32
B. KLI= 32
LI=64
C. KLI=64
LI=64
D. KLI=64
LI=128

Answer 1

The picture in the attached figure

we know that
The inscribed angle measures half of the arc it comprises
so
∠ GHL=(1/2)*[arc LI]
∠ GHL=32°
32°=(1/2)*arc LI
arc LI=32°*2-------> arc LI=64°        

∠KLI=(1/2)*[arc LI]-----> ∠KLI=(1/2)*64°-----> ∠KLI=32°

the answer is the option
B. KLI= 32
LI=64