Question

In a right angled triangle where m∠A= 90° and AB=AC. What is the values of ∠ B. *

2 points

45°

35°

75°

65°

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Answer 1

Step-by-step explanation:

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AB=AC [Given ]

∠A=90°

∴ ∠C=∠B [ Angles opposite to equal sides are equal ] ---- ( 1 )

In △ABC,

∠A+∠B+∠C=180°

[ Angles sum property of triangles ]

⇒ 90° +∠B+∠C=180°

⇒ 90°+∠B+∠B=180°

[ From ( 1 ) ]

⇒ 2∠B=90°

⇒ ∠B=45`

∴ ∠B=∠C=45°

Answer 2

Given :

• angle A = 90°

• AB=AC

To find :

• the value of ∠ B

Concept used :

• Sum of all angles of triangle = 180°

Solution :

It is given that AB=AC and ∠A= 90° , therefore it is right isosceles triangle.

∠C = ∠B ( since AB=AC )

Let ∠C = ∠B be x°

Now according to the question :-

90° + x + x = 180°

90° + 2x = 180°

2x = 180°- 90°

2x = 90°

x = 90°/2

x = 45°

Therefore ∠B = 45°

Answer : 45°