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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 $\angle A=$?

Option 1: 83°

Option 2: 85°

Option 3: 95°

Option 4: 75°


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 26th Jan, 2024

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,
$A+B+C=180^\circ$
⇒ $45^{\circ}+B+B+B-15^{\circ}=180^{\circ}$
⇒ $3B+30^\circ = 180^\circ$
⇒ $B = 50^\circ$
Now, $A=45^{\circ}+B= 45^{\circ}+50^\circ= 95^\circ$
Hence, the correct answer is $95^\circ$

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