<J and <M are base angles of isosceles trapezoid JKLM. If m<J= 22x+5 and m<M = 18x+17, find m<k/
3 degrees
109 degrees
151 degrees
71 degrees
To find the measure of angle K, we can use the fact that the sum of the angles in any quadrilateral is 360 degrees.
Since J and M are base angles of an isosceles trapezoid, they are congruent:
m<J = m<M
Setting the two expressions equal to each other:
22x+5 = 18x+17
Subtracting 18x and 5 from both sides:
4x = 12
Dividing both sides by 4:
x = 3
Now we can substitute this value of x back into the given expressions for m<J and m<M:
m<J = 22(3) + 5 = 66 + 5 = 71
m<M = 18(3) + 17 = 54 + 17 = 71
Since the measures of m<J and m<M are equal, angle K must also measure 71 degrees.
Therefore, m<K = 71 degrees.