The measure of angle K is 128°
STEP - BY - STEP EXPLANATION
What to find?
The measure of angle K.
Given:
measure of angle J = (2x + 9)°
measure of angle M = (6x -1) °
To solve, we need to first make a sketch of the parallelogram
From the sketch above, observe that angle J and angle M are consecutive.
To find the value of x, add measure of J and K and equate to 180.
That is;
J + K = 180 (Consecutive angles)
(2x + 9) +(6x - 1) = 180
Collect like term
2x + 6x = 180 - 9 + 1
8x = 172
Divide both-side of the equation by 8.
x = 21.5
Substitute the value of x into angle M.
That is;
angle M = 6x - 1
= 6(21.5) - 1
=129 - 1
=129
angle M is 128°
Also observe from our sketch that angle K = angle M.
Therefore, the measure of angle K is 128°
