Question

ABCD is a square, what is the measure angle of BAC

Answer 1

45 degrees, you are cutting the right angle in half

Answer 2

measure of ∠BAC is 45°

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°