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0 votes
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in Quadrilaterals by (36.7k points)
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In the square ABCD, ∠BAC = ……………..

A) 70° 

B) 45° 

C) 80° 

D) 60°

2 Answers

+1 vote
by (57.0k points)
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Best answer

Correct option is (B) 45°

\(\because\) AB = BC (sides of square ABCD)

\(\therefore\) \(\triangle ABC\) is an isosceles triangle.

\(\therefore\) \(\angle BAC\) = \(\angle ACB\)   ______(1)   (Opposite angles of equal sides are equal)

Now in \(\triangle ABC\)\(\angle ABC\) = \(90^\circ\)   (angle in square)

Also, \(\angle ABC+\angle BAC+\angle ACB\) \(=180^\circ\)  (Sum of angles in a triangle)

\(\Rightarrow\) \(90^\circ+\) \(2\angle BAC\) \(=180^\circ\)   (From equation (1))

\(\Rightarrow\) \(2\angle BAC\) \(=180^\circ-90^\circ\) \(=90^\circ\)

\(\Rightarrow\) \(\angle BAC\) \(=\frac{90^\circ}2\) = \(45^\circ\)

+2 votes
by (38.9k points)

Correct option is B) 45°

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