Question

in circle n, \\(\overline{kl} \cong \overline{ml}\\). what is the measure of \\(\widehat{jm}\\)? \\(\bigcirc\\ 77^\circ\\) \\(\bigcirc\\ 90^\circ\\) \\(\bigcirc\\ 132^\circ\\) \\(\bigcirc\\ 154^\circ\\) (the diagram shows a circle n with points j, k, l, m on the circumference. arcs and angles are labeled: arc jk is \\((5x + 24)^\circ\\), arc kl is \\((7x + 7)^\circ\\), arc lm is \\((8x - 3)^\circ\\), arc mj is \\((13x + 2)^\circ\\), and there are triangles inside the circle with center n.)

Explanation:

Step1: Set equal congruent arcs

Since $\overline{KL} \cong \overline{ML}$, their corresponding arcs are congruent:
$7x + 7 = 8x - 3$

Step2: Solve for x

Rearrange to isolate x:
$7 + 3 = 8x - 7x$
$x = 10$

Step3: Calculate arc $\overset{\frown}{JM}$

Substitute $x=10$ into the arc expression:
$13x + 2 = 13(10) + 2$

Answer:

132°