Final answer:
By setting the expressions for the base angles J and M of the isosceles trapezoid equal to each other (21x + 4 = 14x + 10), we can solve for x and find that x = 6/7. We confirm this value by checking the measure of the non-base angle K.
Step-by-step explanation:
To solve for x in the isosceles trapezoid JKLM where J and M are the base angles, we must recognize that the sum of the angles in any quadrilateral is 360 degrees. Since JKLM is an isosceles trapezoid, we know that base angles J and M are equal, which means that m/_J = m/_M. Therefore, we can set the expressions for these angles equal to each other to solve for x:
m/_J = 21x + 4 and m/_M = 14x + 10.
By setting them equal, we get:
21x + 4 = 14x + 10
Subtract 14x from both sides to get:
7x + 4 = 10
Now, subtract 4 from both sides to find:
7x = 6
Finally, divide by 7 to get:
x = 6/7
Now that we have the value of x, we can confirm it by checking the measure of angle K. We were given m/_K = 12x - 8, and with x = 6/7:
m/_K = 12(6/7) - 8
m/_K = 72/7 - 8
m/_K = 72/7 - 56/7
m/_K = 16/7 (which is, as expected, not equal to angles J or M, since angle K is a non-base angle of the isosceles trapezoid)