Question

the angle by which \\( \overline { a b } \\) turns clockwise about point b to coincide with \\( \overline { b c } \\) is \\( \square \\) 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 116.1 degrees.

Explanation:

Step1: Calculate the clockwise rotation angle

The angle for \(AB\) to turn clockwise about \(B\) to coincide with \(BC\) is the sum of the two given angles.

$$30.6^{\circ}+33.3^{\circ}$$

$$= 63.9^{\circ}$$

Step2: Calculate the counter - clockwise rotation angle

Since \(B\), \(E\), and \(C\) are on the same straight line, the angle for \(AB\) to turn counter - clockwise to coincide with \(BE\) is \(180^{\circ}-63.9^{\circ}\)

$$180 - 63.9$$

$$=116.1^{\circ}$$

Answer:

The angle by which \(\overline{AB}\) turns clockwise about point \(B\) to coincide with \(\overline{BC}\) is \(63.9\) degrees. The angle by which \(\overline{AB}\) turns counterclockwise to coincide with \(\overline{BE}\) is \(116.1\) degrees.