Question

Find the measure of the are or angle indicated. Assume that lines which appear tanget are tangents​

Answer 1

Given:

In a circle, two chords AK and LJ intersect each other inside the circle at M.

Measure of arc AJ = 65 degrees.

Measure of arc KL = 85 degrees.

To find:

The measure of angle KML.

Solution:

Intersecting chords theorem: According to this theorem, if two chords intersect each other inside the circle then the measure of angle on the intersection is half of the sum of intercepted arcs.

Using Intersecting chords theorem, we get

$m\angle KML =\dfrac{1}{2}(arcKL+arcAJ)$

$m\angle KML =\dfrac{1}{2}(85^\circ +65^\circ )$

$m\angle KML =\dfrac{1}{2}(150^\circ )$

$m\angle KML =75^\circ$

Therefore, the measure of angle KML is 75 degrees.