Question

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

Explanation:

Step1: Properties of a square

In square \(ABCD\), \(AB = BC\) (all sides of a square are equal), and \(\angle ABC=90^{\circ}\) (all angles in a square are right - angles).

Step2: Triangle \(ABC\)

Since \(AB = BC\) and \(\angle ABC = 90^{\circ}\), \(\triangle ABC\) is an isosceles right - triangle.
In an isosceles right - triangle \(\triangle ABC\) with \(\angle ABC = 90^{\circ}\), using the angle - sum property of a triangle (\(\angle BAC+\angle ABC+\angle BCA=180^{\circ}\)) and \(\angle BAC=\angle BCA\) (because \(AB = BC\)), we substitute \(\angle ABC = 90^{\circ}\) into the formula:

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Answer:

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