Calculate the smaller side of a rectangular trapezoid with an angle of 135 degrees. The base difference is 7 cm.

univerkov | February 9, 2021 | education

From the vertex C of the trapezoid, draw the height CH, then the angle DСН= ВСD – ВСН = 135 – 90 = 45.

The right-angled triangle СDН is isosceles, since one of its acute angles is 45.

Then CH = DН.

By condition, AD – BC = 7 cm, and since BC = AН, then AD – AН = DН = 7 cm.

Then DН = CH = 7 cm, and therefore AB = 7 cm, since ABCH is a rectangle.

Answer: The length of the smaller side is 7 cm.

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