Question

In the figure given below, (i) find the value of x. (ii) find the measures of BOC and AOC.​

Answer 1

Given that,

Angle AOC+ Angle BOC+ Angle BOD=338°

We know that

Sum of all angles is 360

Angle AOC+ Angle BOC+ Angle BOD + Angle AOD = 360

338 + angle AOD = 360 ( Acc. to Question)

Angle AOD = 360-338 =22

Angle AOD = angle BOC (Because they are vertically opposite angles)

They are equal to 22

And

Angle BOC + angle BOD = 180 ( Because linear pair...sum of those angles will be 180)

22+angle BOD = 180

Angle BOD = 180-22

Angle BOD = 158

Angle BOD = Angle AOC = 158 (Because vertically opposite angles are equal)

Angle AOC = 158

Angle BOC = 22

Angle AOD = 22

Angle BOD = 158