<J and <M are base angles of isosceles trapezoid JKLM. If m<J= 22x+5 and m<M = 18x+17, find m<k/
Since JKLM is an isosceles trapezoid, the base angles <J and <M must be congruent. Therefore, we can set the two angle measures equal to each other:
22x + 5 = 18x + 17
Next, we can solve this equation for x:
22x - 18x = 17 - 5
4x = 12
Divide both sides by 4 to isolate x:
x = 3
Now that we have the value of x, we can substitute it back into one of the angle measures to find the measure of <J (or <M). Let's use the first equation:
m<J = 22x + 5
m<J = 22(3) + 5
m<J = 66 + 5
m<J = 71
Therefore, the measure of <J is 71 degrees.
Since JKLM is an isosceles trapezoid, this means that the base angles are supplementary. In other words, <J + <K = 180 degrees. So to find the measure of <K, we can subtract the measure of <J from 180:
m<K = 180 - m<J
m<K = 180 - 71
m<K = 109
Therefore, the measure of <K is 109 degrees.