ABCD-rectangular trapezoid angle A = 90 angle C-angle D = 48. Find all angles.

Decision:

We will use the fact that the sum of two internal one-sided angles at the intersection of parallel secant lines is 180 degrees.

1 case. The bases of the trapezoid are BC and AD.

angle B = 180 – angle A = 180 – 90 = 90 degrees.

Let the angle D = x, then the angle C = x +48.

angle C + angle D = 180, we get the equation:

x + x + 48 = 180;

2x = 180 – 48;

2x = 132;

x = 132: 2;

x = 66.

angle D = 66 degrees,

angle C = 66 + 48 = 114 degrees.

2 case. The bases of the trapezoid are AB and CD.

angle D = 180 – angle A = 180 – 90 = 90 degrees,

angle C = angle D + 48 = 90 + 48 = 138 degrees,

angle B = 180 – angle C = 180 – 138 = 42 degrees.

Answer: 90, 90, 114, 66 degrees or 90, 42, 138, 90 degrees.