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.
<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
1 answer