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
75.5 o
To find the measure of angle K in an isosceles trapezoid, we first need to know that the sum of the base angles (angle J and angle M) of an isosceles trapezoid is equal to 180 degrees.
Therefore, we can set up the equation:
20x + 9 + 14x + 15 = 180
34x + 24 = 180
34x = 156
x = 4.59
Now, we can substitute x back into angle J to find its measure:
20(4.59) + 9 = 97.8
Since angle J and angle K are congruent as base angles of the isosceles trapezoid, angle K will also be 97.8 degrees.
Therefore, the measure of angle K is 97.8 degrees.
None of the provided answer choices match the correct value, so the closest answer is 75.5 degrees. However, the correct answer is 97.8 degrees.