One of the angles of an isosceles trapezoid is 168 degrees, find the rest of the angles.

A trapezoid is a quadrangle with two parallel sides, bases. The other two sides are called lateral, if they are equal, then the trapezoid is isosceles.

In an isosceles trapezoid, the angles at one base are equal, and the angles at different bases add up to 180 degrees, since they are internal one-sided when two parallel straight lines intersect the third.

If the trapezoid ABCD, BC and AD of the base, AB = CD, then

angle A = angle D, angles at the base AD.
angle B = angle C, angles at the base of the BC.
angle A + angle B = angle C + angle D = 180 °.
Let the angle A = angle D = 168o, then

angle A + angle B = 180 °.

angle B = angle C = 180 ° – angle A = 180 ° – 168 ° = 12 °.

Answer: the angles are equal to 168o, 168o, 12o, 12o.

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