The sum of the two angles of an isosceles trapezoid is 268. Find the larger angle of the trapezoid.

Let there be given an isosceles trapezoid ABCD with acute angles at the lower base AD, which, by the property of an isosceles trapezium, will be equal to ∠ BAD = ∠ CDA. Consider the one-sided corners for the BAD angle. ∠ BAD + ∠ CDA <180 °, as they are sharp. ∠ BAD + ∠ ABC = 180 °, since they are internal one-sided at BC | | AD and secant AB. The obtuse angle ABC remains. By the property of an isosceles trapezoid, the angles at the upper base ∠ ABC = ∠ BCD will be equal. Hence, the sum of these two angles of an isosceles trapezoid can be equal to 268 °; ∠ ABC + ∠ BCD = 268 °; ∠ ABC = 268 °: 2; ∠ ABC = 134 °
Answer: The larger trapezoid angle is 134 °.