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Question
ABC is a right angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
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Solution
Given that ABC is a right angled triangle such that ∠A = 90° and AB = AC Since,
AB = AC ⇒ ΔABC is also isosceles
∴ We can say that ΔABC is right angled isosceles triangle
⇒ ∠C=∠B and ∠A=90° ................(1)
Now, we have
Sum of angled in a triangle =180°
⇒ ∠A+∠B+∠C=180°
⇒ 90°+∠B+∠B=180° [∵ From (1)]
⇒ 2∠B=180°-90°
⇒`∠B=(90°)/2=45°`
∴ ∠B=∠C=45°
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