<J and <M are base angles of isosceles trapezoid JKLM. If m<J= 22x+5 and m<M = 18x+17, find m<k
A. 109 degrees
B. 71 degrees
C. 3 degrees
D. 151 degrees
Since JKLM is an isosceles trapezoid, angles J and M are congruent. So, we set up an equation:
22x + 5 = 18x + 17
4x = 12
x = 3
Now we can find the measure of angle J:
m<J = 22x + 5 = 22(3) + 5 = 71 degrees
And the measure of angle M:
m<M = 18x + 17 = 18(3) + 17 = 71 degrees
Since angles J and M are congruent, we can find the sum of these angles:
m<K = 180 - 2(71) = 180 - 142 = 38 degrees.
Therefore, the measure of angle K is 38 degrees.
The answer is not listed among the options.