Question
<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
151 degrees 151 degrees 3 degrees 3 degrees 109 degrees 109 degrees 71 degrees 71 degrees
Answers
GPT 3.5
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.
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.