angle j and Angle Mare base angles of isosceles trapezoid JKLM. If Measure of angle J equals 20 x plus 9and Measure of angle M equals 14 x plus 15, find measure of angle k.
Isosceles trapezoid J K L M is shown.
(1 point)
Responses
151o
151 o
1o
1 o
29o
29 o
75.5o
To find the measure of angle K in the isosceles trapezoid JKLM, we can use the fact that the base angles of an isosceles trapezoid are congruent.
Since J and M are the base angles, we have:
20x + 9 = 14x + 15
Subtracting 14x from both sides:
6x + 9 = 15
Subtracting 9 from both sides:
6x = 6
Dividing both sides by 6:
x = 1
Now we can substitute this value of x back into either of the expressions for angle J or M to find the measure of angle K. Let's use angle J:
Measure of angle J = 20x + 9
Measure of angle J = 20(1) + 9
Measure of angle J = 20 + 9
Measure of angle J = 29
So, the measure of angle K is 29 degrees.