The measure of angle K is 151 degrees.
Given that J and M are the base angles of an isosceles trapezoid, we know that they are equal:
m<J = m<M
Substituting the given values for the measures of these angles, we have:
20x + 9 = 14x + 15
Solving for x, we get:
6x = 6
x = 1
Substituting this value of x back into the given expression for the measure of angle J, we have:
m<J = 20(1) + 9 = 29
Since the trapezoid is isosceles, we know that the non-base angles, K and L, are also equal:
m<K = m<L
The sum of the angles in a quadrilateral is 360 degrees, so we can write the following equation:
m<J> + m<K> + m<L> + m<M> = 360
Substituting the values we now know for the measures of angles J and M, we get:
29 + m<K> + m<L> + 29 = 360
Combining like terms, we have:
m<K> + m<L> = 302
Since we know that the measures of angles K and L are equal, we can divide both sides of this equation by 2 to find the measure of angle K:
m<K> = \frac{1}{2} (302) = 151
Therefore, the measure of angle K is 151 degrees.
Question
angle J and angle m are base angles of isosceles trapezoid JKLM. If m angle J = 20x+9 and m angle m = 14x+15, find m angle k.