Question

In a triangle ABC, ∟A – ∟B = 32° and ∟B - ∟C =41°, then ∟B =? option are- 43° 34° 63° 71°

Answer 1

Solution :-

Given

∠A - ∠B = 32°

Simplifying

∠A = 32° + ∠B

Assuming as equation 1

∠B - ∠C = 41°

Simplifying

∠C = ∠B - 41°

Assuming as equation 2

Now, using angle sum property of a ∆

∠A + ∠B + ∠C = 180°

→ 32° + ∠B + ∠B + ∠B - 41° = 180°

→ 3∠B - 9° = 180°

→ 3∠B = 189°

→ ∠B = 189° ÷ 3

→ ∠B = 63°

Hence , ∠B = 63° . So , option C is your answer

More information :-

Properties :-

• Angle sum property :- Sum of all angles in a ∆ = 180°
• Exterior angle property :- Exterior angle equal to sum of two interior opposite angles .

Types of ∆'s

• Obtuse ∆ :- A ∆ having one obtuse angle .
• Acute ∆ :- A ∆ having all sides equal
• Isosceles ∆ :- A ∆ having 2 equal sides
• Right ∆ :- A ∆ having one right angle

Answer 2

Answer:

✡ Question ✡

➡ In a triangle ABC,∠A – ∟B = 32° and ∠B - ∠C =41°, then ∠B =?

✡ Given ✡

➡ In a triangle ABC,∠A – ∟B = 32° and ∠B - ∠C =41°.

✡ To Find ✡

➡ ∠B = ?

✡ Solution ✡

▶ ∠A - ∠B = 32°

=> ∠A = 32° + ∠B ....... Equation (1)

▶ ∠B - ∠C =41°

=> ∠C = ∠B - 41° ......... Equation (2)

✴ According to the question,

⭐ ∠A + ∠B + ∠C = 180° ⭐

=> 32°+∠B+∠B+∠B-41°=180°

=> 3∠B - 9° = 180°

=> 3∠B = 180° + 9°

=> 3∠B = 189°

=> ∠B = $\dfrac{189°}{3}$

=> ∠B = 63°

∴ ∠B = 63° (3) is the correct option.

Step-by-step explanation:

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