Question

The angle by which AB turns clockwise about point B to coincide with BC is ? 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 AB turns counterclockwise to coincide with BE is ? degrees.

fill in the ? marks

Answer 1

Explanation:

(A) it is given that if AB turns clockwise about point B to coincide with BC, then the angle will be=∠ABD+∠DBC=33.3°+30.6°=63.9°.

(B) 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, then the angle by which AB turns clockwise to coincide with BE is:∠ABE+∠ABD+∠DBC=180° (using the straight line property)

⇒∠ABE+33.3°+30.6°=180°

⇒∠ABE+63.9°=180°

⇒∠ABE=116.1°

Answer 2

a) AB turn clockwise to coincide with BC

= ABD + DBC

= 33.3° + 30.6°

= 63.9°


b) If E is drawn directly opposite C.

EBC is a straight line, so sum of angles =180°

ABE + ABD + DBC = 180°

ABE + 33.3° + 30.6° = 180°

ABE + 63.9° = 180°

ABE = 180 - 63.1

ABE = 116.9°

Hope this explains it.