Question

In circle N, KL ≅ ML. Circle N is shown. Line segments N J, N M, N L, and N K are radii. Lines are drawn to connect each point on the circle to create secants J M, M L, L K, and K J. M L and K L are congruent. The measure of arc J K is (5 x + 24) degrees, the measure of arc J M is (13 x + 2) degrees, the measure of arc M L is (8 x minus 3) degrees, and the measure of arc K L is (7 x + 7) degrees. What is the measure of Arc J M? 77° 90° 132° 154°

Answer 1

Given:

In circle N, KL = ML.

The measure of arc J K is (5 x + 24) degrees,

the measure of arc J M is (13 x + 2) degrees,

the measure of arc M L is (8 x minus 3) degrees, and

the measure of arc K L is (7 x + 7) degrees.

To find:

What is the measure of Arc J M?

Solution:

Consider the attached figure, while going through the following steps.

We know that, sum of interior angles of a circle equals 360°

From given figure, it's clear that,

(5x + 24)° + (7x + 7)° + (8x - 3)° + (13x + 2)° = 360°

33x + 30° = 360°

33x = 360° - 30°

33x = 330°

x = 330°/33

∴ x = 10°

Now consider, Arc JM

(m Arc JM) = (13x + 2)°

(m Arc JM) = [13 × 10 + 2]°

∴ (m Arc JM) = 132°

Answer 2

Answer:

132

Step-by-step explanation:

yes