Question

What is the missing angle

Answer 1

`Answer ☘️`

★ Important points to know

`{\boxed{ \bold{Exterior \: Angle \: Theorem : - }}}`

• The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
• 
  `\pink{ ↪ \sf \angle \: C + \angle \: D = \angle \: B}`

★ Let's solve :-

`\sf ↪\angle \: 65 \degree + \angle \: 30 \degree =\angle \:B\\ \\ \sf ↪\angle \: 95 \degree = \angle \:B`

Hence option A 95⁰ is the right ans ✓

`\sf{\:мѕнαcкεя\: ♪...}`

Answer 2

`\sf\large \green{\underbrace{\red{Answer⋆}}}:`

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°