<J and <M are base angles of isosceles trapezoid JKLM. If m<J= 22x+5 and m<M = 18x+17, find m<k/ (1 point) Responses
151 degrees 151 degrees 3 degrees 3 degrees 109 degrees 109 degrees 71 degrees 71 degrees
To find the measure of angle K, we can use the fact that the sum of the interior angles of a trapezoid is 360 degrees.
The formula for the sum of the interior angles of a trapezoid is:
Angle K + Angle J + Angle M + Angle L = 360 degrees
Since J and M are base angles of an isosceles trapezoid, they have equal measures:
m<J = m<M
Therefore, we can write:
m<K + (22x + 5) + (18x + 17) + m<K = 360
Simplifying the equation, we have:
2m<K + 40x + 22 = 360
Subtracting 22 from both sides, we have:
2m<K + 40x = 338
Subtracting 40x from both sides, we have:
2m<K = 338 - 40x
Dividing both sides by 2, we have:
m<K = (338 - 40x) / 2
Therefore, the measure of angle K is (338 - 40x) / 2.