Question

Finding KLM in this problem, if you could also explain it, that would be nice :)

Answer 1

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.

$\Rightarrow\angle KLM=\frac{1}{2}(m(ar \ JN)-m(ar \ KM))$

$\Rightarrow\angle KLM=\frac{1}{2}(140^\circ-66^\circ)$

$\Rightarrow\angle KLM=\frac{1}{2}(74^\circ)$

$\Rightarrow\angle KLM=37^\circ$

The measure of angle KLM is 37°.