Question

IN THE GIVEN FIGURE
a). IS ∆BOC ADJACENT TO ∆BOA ? ( GIVE REASON ALSO )
b). IS ∆ BOC ADJACENT TO ∆COB ?
( GIVE REASON ALSO )

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Answer 1

Answer:

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they have a common vertex (O).

they have a common arm (OB) and the other arms OA and OC of the two angles are on opposite sides of the common arm OB.

Answer 2

Yes, ∠BOC is adjacent to ∠BOA

NO ,  ∠BOC is not adjacent to ∠COB

Given:

• A common point O
• Rays OA , OB and OC
• Ray OB is in between Rays OA and OC

To Find:

• Is ∠BOC adjacent to ∠BOA
• Is ∠BOC adjacent  to ∠COB

Solution:

Angles that have a common vertex and a common side are called adjacent angles.

The angles must not overlap.

∠BOC and ∠BOA have common vertex O and a common side OB

Hence These are adjacent angles.

Yes, ∠BOC is adjacent to ∠BOA

∠BOC and ∠COB have common vertex O and  common side OB  and OC

Hence These are Overlapping angles.

As angles are overlapping so these are not adjacent angles.

NO ,  ∠BOC is not adjacent to ∠COB

(correction in Question ∆ symbol should have been ∠ )

Yes, ∠BOC is adjacent to ∠BOA

NO ,  ∠BOC is not adjacent to ∠COB