Question

If m∠jkl = (8x – 6)° and measure of arc jml = (25x – 13)°, find measure of arc jml.

Answer 1

Applying the angle of intersecting secants theorem, the measure of arc JML is: 262°.

What is the Angle of Intersecting Secants Theorem?

The angle of intersecting secants theorem states that when two lines form an external angle outside a circle, the measure of the angle is half the difference between the measure of the major and minor intercepted arcs.

Thus:

m∠JKL = (measure of arc JML - measure of arc JL)/2 => angle of intersecting secants theorem

m∠JKL  = 8x - 6

measure of arc JML = 25x - 13

measure of arc JL = 360 - (25x - 13)

Plug in the values

8x - 6 = [(25x - 13) - (360 - (25x - 13))/2]

Solve for x

2(8x - 6) = [(25x - 13) - (360 - 25x + 13)]

16x - 12 = [(25x - 13) - (373 - 25x)]

16x - 12 = 25x - 13 - 373 + 25x

16x - 12 = 50x - 386

16x - 50x = 12 - 386

-34x = -374

x = 11

Measure of arc JML = 25x - 13

Plug in the value of x

Measure of arc JML = 25(11) - 13 = 262°

Learn more about angle of intersecting secants theorem on:

brainly.com/question/1626547