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In a right angled triangle where angle A= 90° and AB=AC. What are the values of angle B.
- a)45°
- b)35°
- c)75°
- d)65°
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In a right angled triangle where angle A= 90° and AB=AC. What are ...
∵ In ∆ABC,
AB = AC
∴ ∠B = ∠C ...(1)
| Angles opposite to equal sides of a triangle are equal
In ∆ABC,
∠A + ∠B + ∠C = 180°
| Sum of all the angles of a triangle is 180°
⇒ 90° + ∠B + ∠C = 180°
| ∵ ∠A = 90° (given)
⇒ ∠B + ∠C = 90° ...(2)
From (1) and (2), we get
∠B = ∠C = 45°.
AB = AC
∴ ∠B = ∠C ...(1)
| Angles opposite to equal sides of a triangle are equal
In ∆ABC,
∠A + ∠B + ∠C = 180°
| Sum of all the angles of a triangle is 180°
⇒ 90° + ∠B + ∠C = 180°
| ∵ ∠A = 90° (given)
⇒ ∠B + ∠C = 90° ...(2)
From (1) and (2), we get
∠B = ∠C = 45°.
Most Upvoted Answer
In a right angled triangle where angle A= 90° and AB=AC. What are ...
In a right-angled triangle, one angle is always 90 degrees. This angle is denoted as angle A. The other two angles are acute angles, meaning they are less than 90 degrees. These acute angles are denoted as angle B and angle C.
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Community Answer
In a right angled triangle where angle A= 90° and AB=AC. What are ...
Angle A is 90 degree Angle AB=Angle AC. Therefore Angle B=Angle C Angle B+C+A= 180 degree.Angle A is = 90 degree. Angle B= Angle C .Angle B+C = 180 degree - Angle A. Angle B+C = 180 degree-90 degree= 90 degree. As it is given Angle B is equal to Angle C, Angle B = 90 degree/2=45 degree.Since Angle B = Angle C, Angle C = 45 degree
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