One day Hemesh was going on a road trip with his father. They started . . .

Case Study Based Question on Lines and Angles

One day Hemesh was going on a road trip with his father. They started their journey on a straight road. Later walking some distance they reach a crossroad where one straight road intersects another at 45° as shown in figure. 

Based on above information, answer the following questions :

(i) Find the measure of ∠BOC

(ii) Find the measure of ∠BOD

(iii) Find the reflex ∠BOC

OR

Vertically opposite angles have common arms, Is it true?

Detailed Solution : 

(i) ∠AOC + ∠BOC = 180°
45°+∠BOC = 180°
∠BOC = 180°-45°

∠BOC = 135°

(ii) ∠BOD=∠AOC [Vertically opposite angles]

∠BOD=45° [∵∠AOC=45°]

(iii) Reflex ∠BOC
= 360°-∠BOC 
=360°-135°
= 225°

Hence, Reflex ∠BOC=225°

OR

False, vertically opposite angles do not have common arms. Adjacent angles and linear pairs of angles have common arms.