### Instruction: The acute angles of a particular isosceles trapezoid each measure 40 degrees. What is the measure, in degrees, of each obtuse angle in the trapezoid?### Response: I know that an isosceles trapezoid is a quadrilateral with two parallel bases and two congruent legs.
I also know that the sum of the interior angles of any quadrilateral is 360 degrees.
Let me label the acute angles as A and the obtuse angles as B, and draw a diagram of the trapezoid.
Since the trapezoid is isosceles, the base angles are congruent, so A = A and B = B.
I can use the fact that the sum of the interior angles is 360 degrees to write an equation: A + A + B + B = 360.
I can simplify this equation by using the fact that A = 40, so 40 + 40 + B + B = 360.
I can combine like terms and subtract 80 from both sides, so 2B = 280.
I can divide both sides by 2, so B = 140.
This means that each obtuse angle in the trapezoid measures 140 degrees.