Question

One pair of base angles of an isosceles trapezoid each have a measure of 37x - 6. The other pair of base angles of the trapezoid each have a measure of 22x + 9. What is the value of x?

Answer 1

To find the value of x in the given isosceles trapezoid, set up an equation using the fact that the sum of the base angles is 180 degrees. Simplify and solve for x.

Step-by-step explanation:

To find the value of x, we can set up an equation using the fact that the sum of the base angles of an isosceles trapezoid is equal to 180 degrees. Since the two pairs of base angles are given, we can set up the equation: (37x - 6) + (37x - 6) + (22x + 9) + (22x + 9) = 180. Simplifying the equation, we get: 118x + 6 = 180. Solving for x, we subtract 6 from both sides: 118x = 174. Finally, we divide both sides by 118 to find the value of x: x ≈ 1.47.