Question : A, B, and C are three angles of a triangle. If $A - B = 45^{\circ}$ and $B - C = 15^{\circ}$ then $∠ A =$ ?
Option 1: 83°
Option 2: 85°
Option 3: 95°
Option 4: 75°

Question

Question : $∠ A, ∠ B$ and $∠ C$ are three angles of a triangle. If $∠ A - ∠ B = 15^{\circ}, ∠ B - ∠ C = 30^{\circ}$ , then $∠ A, ∠ B$ and $∠ C$ are:

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Answer 1

Correct Answer: 95°

Solution : Given, $A - B = 45^{\circ}$
And $B - C = 15^{\circ}$
So, $A = 45^{\circ} + B$
And, $C = B - 15^{\circ}$
By the angle sum property of a triangle,
$A + B + C = 180^{\circ}$
⇒ $45^{\circ} + B + B + B - 15^{\circ} = 180^{\circ}$
⇒ $3 B + 30^{\circ} = 180^{\circ}$
⇒ $B = 50^{\circ}$
Now, $A = 45^{\circ} + B = 45^{\circ} + 50^{\circ} = 95^{\circ}$
Hence, the correct answer is $95^{\circ}$

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Question : A, B, and C are three angles of a triangle. If A−B=45∘ and B−C=15∘ then ∠A=?Option 1: 83°Option 2: 85°Option 3: 95°Option 4: 75°

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Question : A, B, and C are three angles of a triangle. If $A - B = 45^{\circ}$ and $B - C = 15^{\circ}$ then $∠ A =$ ?
Option 1: 83°
Option 2: 85°
Option 3: 95°
Option 4: 75°