Answer:
measure of ∠BAC is 45°
Step-by-step explanation:
We have Square ABCD
we need to find the measure of ∠BAC
Let us take ΔBAC
We know that all the angles in a square is equal to 90°
Therefore ΔBAC is right angled triangle since ∠ABC= 90°
Sum of angles in a triangle = 180°
∠ABC + ∠BCA + ∠BAC = 180°
90° + ∠BCA + ∠BAC =180° ( since ∠ABC= 90°)
∠BCA + ∠BAC =180° -90° ( subtracting 90° from both sides)
∠BCA + ∠BAC = 90°
sides of square are equal so AB = BC and angles opposite to equal sides are equal hence ∠BCA = ∠BAC
so we have
∠BAC+∠BAC = 90°
2∠BAC = 90°
∠BAC = 45° ( divide both sides by 2)
so we have measure of ∠BAC is 45°
