Question

In the given figure ,twostraight lines AB and XD intersect at a point O.If <AOC=42,find the measure of the angles:
1)<AOD
2)<BOD
3)<COB​

Answer 1

Answer:

Angle AOC = 42°

i.) Let Angle AOD be x.

Angle AOC + Angle AOD = 180°

[As, Angle AOC and Angle AOD lies on a straight line]

42° + x = 180°

x = 180° - 42°

x = 138°

Angle AOD = x = 42°

ii.) Angle BOD = Angle AOC = 42°

[Vertically opposite angles]

iii.) Angle COB = Angle AOD = 42°

[Vertically opposite angles]

Answer 2

Answer:

i) 138°

ii) 42°

iii) 138°

Step-by-step explanation:

i) Angle AOC + Angle AOD = 180° (Angles on a straight line = 180°)

42 + AOD = 180

AOD = 180 - 42 = 138

Angle AOD = 138°

ii) Angle BOD = Angle AOC (Vertically opposite angles)

Angle BOD = 42°

iii) Angle COB = Angle AOD (Vertically opposite angles)

Angle COB = 138°

Hope it helps you:)