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 GE and JF intersect each other inside the circle at D.

Measure of arc EF = 90 degrees.

Measure of arc JG = 70 degrees.

To find:

The measure of angle EDF.

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

$m\angle EDF =\dfrac{1}{2}(arcEF+arcJG)$

$m\angle EDF =\dfrac{1}{2}(90^\circ +70^\circ )$

$m\angle EDF =\dfrac{1}{2}(160^\circ )$

$m\angle EDF =80^\circ$

Therefore, the measure of angle EDF is 80 degrees.