In square $ABCD$, what is the measure of angle $\angle BAC$?

• A. $45°$
• B. $90°$
• C. $30°$
• D. $60°$

Answer: (A)

Verified step by step guidance

1. Identify the points involved: A, B, and C are vertices of the square ABCD. Since ABCD is a square, all sides are equal and all angles are 90°.
2. Visualize or draw the square ABCD and mark points A, B, and C. Note that angle \( \angle BAC \) is the angle at vertex A formed by points B and C.
3. Recall that in a square, the diagonal divides the square into two congruent right isosceles triangles. The diagonal AC connects vertices A and C.
4. Since triangle ABC is right isosceles (because AB = BC and angle ABC = 90°), the angles at B and C are 45° each, and the angle at A between B and C is also 45°.
5. Therefore, the measure of \( \angle BAC \) is 45°, because it is the angle between the two sides AB and AC of the square.