Question

If m JKM = 43', mMKL = (8x – 20)", and mZJKL = (10x - 11)", find each

measure.
M
J
K
X=
mZMKL =
mZJKL =

Answer 1

To find the angle measures, we solve for x using the given equations and knowing the sum of angles in a straight line is 180 degrees. After finding x, we calculate the measures of the angles. Angle JKL was calculated by subtracting the sum of angles JKM and MKL from 360 degrees.

Step-by-step explanation:

The student is asking to solve for the measures of angles in a geometric figure given their expressions in terms of x. The measure of angle JKM is given as 43 degrees, the measure of angle MKL is given as (8x – 20) degrees, and the measure of angle JKL is given as (10x - 11) degrees. To find the values of these angles, we must use the fact that the sum of angles in a triangle is 180 degrees.

Since angles JKM and MKL form a straight line, they sum up to 180 degrees. We can set up the equation:

43 + (8x - 20) = 180

Solving for x will allow us to find the measure of angle MKL and JKL. To do this:

1. Add 20 to each side of the equation: 43 + 20 + 8x = 200
2. Combine like terms: 63 + 8x = 200
3. Subtract 63 from both sides: 8x = 137
4. Divide by 8: x = 17.125 or 17¹⁄₈ in simplified form

Now that we have the value of x, we can calculate the measures of MKL and JKL:

mMKL = 8(17.125) - 20 = 136.75

And since the angle JKL is a full circle (360 degrees), containing the straight line JKM, and the angles JKM and MKL, we have:

mZJKL = 360 - (mJKM + mMKL)

Inserting the values, we get:

mZJKL = 360 - (43 + 136.75) = 360 - 179.75 = 180.25 degrees