<j and <m are base angles of isosceles trapezoids jklm if m<j = 22x + 5 and m<m = 18x+17 find m<k/
Since JKL is an isosceles trapezoid, the base angles, <J and <K, are congruent. So, <M<K is also true since <M is the adjacent angle to both <J and <K.
We have two given angles:
<M<J = 22x +5
<M<M = 18x + 17
Since <M<J = 22x +5, and we know that <M<M, then <M is the smaller angle. So we can set up the inequality:
<M<M
22x + 5 < 18x + 17 [since 18x +17 is the larger angle]
Simplifying the inequality:
22x - 18x < 17 - 5
4x < 12
x < 12/4
x < 3
Now we can find the value of <M:
<M<J = 22x + 5 [given]
<M<J = 22(3) + 5 [since x < 3]
<M<J = 66 + 5
<M<J = 71
Since <M<J = 71, we know that <M<K is also 71 degrees.
Therefore, m<k = <M<K = 71 degrees.