To find :-
The angle ∠ABC = ?
Given :-
∠BCD = 65°
∠BDC = 30°
Solution :-
Firstly we have to find ∠CBD, with the help of ∠CBD, we will able to find ∠ABC.
To find ∠CBD, we will use angle sum formula
(=> The sum of angles of all 3 sides of triangle is equal to 180°).
∠CBD + ∠BCD + ∠BDC = 180° (angle sum property)
∠CBD + 65° + 30° = 180°
∠CBD + 95° = 180°
∠CBD = 180° - 95°
∠CBD = 85°
Now we have ∠CBD, and in the diagram ∠CBD and ∠ABD lies on the same line but it is seperated by line BC, it means they are linear pair and the sum of both angles (∠CBD and ∠ABC) is equal to 180°.
∠ABC + ∠CBD = 180° (linear pair)
∠ABC + 85° = 180°
∠ABC = 180° - 85°
∠ABC = 95°
Result :-
The ∠ABC is 95° by using the above method.
Choose the first option
(A) 95°