Question

Find $m\angle JKM$m∠JKM​ . Triangle J K L is shown. The measure of angle J is x degrees. The measure of angle L is 58 degrees. The measure of external angle J K M is equal to 2 x minus 3 degrees. The measure of angle cap j cap k cap m$\angle JKM$∠JKM​ is $\degree$°​ . Skip to navigation Previous 1 , Fully Attempted. 2 , Unattempted. 3 , Fully Attempted. 4 , Unattempted. 5 , Unattempted. 6 , Unattempted. 7 , Unattempted. 8 , Unattempted. 9 , Unattempted.

Answer 1

The measure of angle JKM in the triangle is 119 degrees, calculated by using the external angle theorem and the sum of angles in a triangle.

Step-by-step explanation:

To find $m\angle JKM$ in triangle JKL with the given information, we will use the fact that the sum of the angles in a triangle is 180 degrees. Angle J is given as $x$ degrees, angle L is 58 degrees, and the external angle JKM is given as $2x - 3$ degrees.

Since $\angle JKM$ is an external angle to triangle JKL, it equals the sum of the two non-adjacent internal angles, J and L. Therefore:

$2x - 3 = x + 58$

Now, we can solve for $x$:

$x = 61$ degrees

Finally, we substitute $x$ back into the expression for $\angle JKM$ to find the measure of that angle:

$m\angle JKM = 2(61) - 3$

$m\angle JKM = 119$ degrees