Question

the angle by which \\( \overline { a b } \\) turns clockwise about point b to coincide with \\( \overline { b c } \\) is 30.6 degrees. if from point b, a point e is drawn directly opposite point c so that b, e, and c are on the same straight line, the angle by which \\( \overline { a b } \\) turns counterclockwise to coincide with \\( \overline { b e } \\) is degrees.

Explanation:

Step1: Calculate the total angle for a straight line

A straight - line angle is \(180^{\circ}\).

Step2: Find the required angle

We know that the angle between \(AB\) and \(BC\) (after clock - wise rotation) is \(33.3^{\circ}+30.6^{\circ}\). Let the angle by which \(AB\) turns counter - clockwise to coincide with \(BE\) be \(x\). Then \(x+(33.3^{\circ}+30.6^{\circ}) = 180^{\circ}\).

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Answer:

\(116.1\)