Answer:
The measure of angle J is 44°
Step-by-step explanation:
Isosceles Trapezoid
The isosceles trapezoid has its non-parallel sides of the same length, thus the angles they form with their respective parallel sides are congruent.
It means: Angle J is congruent with angle K and angle M is congruent with angle L
The sum of angles in a trapezoid is 180*(4-2)=360°
Thus:
[tex]m\angle J+m\angle K+m \angle M+m\angle L = 360^\circ[/tex]
[tex]7x+2+7x+2+25x-14+25x-14=360[/tex]
Joining like terms:
[tex]64x-24=360[/tex]
Adding 24:
[tex]64x=384[/tex]
Dividing by 64:
x=6°
Thus:
[tex]m\angle J = 7*6+2=44^\circ[/tex]
[tex]m\angle M = 25*6-14=136^\circ[/tex]
The measure of angle J is 44°
