Question

abcd is a square. what is the measure of angle bac? 30° 45° 60° 90°

Explanation:

Step1: Properties of a square

In square \(ABCD\), \(AB = BC\), and \(\angle ABC=90^{\circ}\).

Step2: Triangle \(ABC\)

Since \(AB = BC\) and \(\angle ABC = 90^{\circ}\), \(\triangle ABC\) is an isosceles right - triangle.
In an isosceles right - triangle \(\triangle ABC\), \(\angle BAC=\angle BCA\).
Using the angle - sum property of a triangle (\(\angle ABC+\angle BAC+\angle BCA = 180^{\circ}\)), substituting \(\angle ABC = 90^{\circ}\) and \(\angle BAC=\angle BCA\), we get \(90^{\circ}+2\angle BAC=180^{\circ}\).
Solving for \(\angle BAC\):

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Answer:

\(45^{\circ}\) (the second option)