# In a rectangular trapezoid, the angle difference at one of the lateral sides is 48 °. Find the corners of the trapezoid.

March 27, 2021 | education

| Given:

rectangular trapezoid ABCE,

angle E – angle C = 48 degrees,

Find the angles of a rectangular trapezoid ABCE, that is, angle A, angle B, angle C, angle E -?

Decision:

Consider a rectangular trapezoid ABCE. Angle A = Angle B = 90 degrees. Angle E = angle C + 48. We know that the sum of the degree measures of the parallelogram is 360 degrees.

Hence:

angle A + angle B + angle C + angle E = 360;

90 + 90 + angle С + angle С + 48 = 360;

180 + 2 * angle С + 48 = 360;

228 + 2 * angle C = 360;

2 * angle С = 360 – 228;

2 * angle C = 132;

angle C = 132: 2;

angle C = 66 degrees;

angle E = 66 + 48 = 114 degrees.

Answer: 90 degrees; 66 degrees; 114 degrees.

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