The measure of angle KLM is 37°.
Solution:
Given data:
m(ar JN) = 140° and m(ar KM) 66°
To find the angle KLM:
If two secants intersect outside a circle, then the measure of angle formed is one half of the difference of the measures of the intercepted arcs.
[tex]$\Rightarrow\angle KLM=\frac{1}{2}(m(ar \ JN)-m(ar \ KM))[/tex]
[tex]$\Rightarrow\angle KLM=\frac{1}{2}(140^\circ-66^\circ)[/tex]
[tex]$\Rightarrow\angle KLM=\frac{1}{2}(74^\circ)[/tex]
[tex]$\Rightarrow\angle KLM=37^\circ[/tex]
The measure of angle KLM is 37°.
