In a quadrilateral ABCD BC = AD BC || AD angle BAC + angle ACD = 80 °. Find these corners.

Given: quadrilateral ABCD, BC = AD, BC || AD, angle BAC + angle ACD = 80 °.

Find: Angles BAC and ACD.

Decision

If BC = AD and these sides are parallel to each other, then the quadrilateral ABCD is a rectangle.

Let the line AC intersect the parallel lines BC and AD. Angles BAC and ACD – angles with parallel lines, as well as secant AC. These angles are cross-lying, and the cross-lying angles are equal, it follows that the angle BAC = angle ACD = 80 ° / 2 = 40 °.

Answer: 40 °, 40 °.