How to Find the Measure of Angle DBC?

If ∠BAC = 45°, what is ∠DBC? 1) 45° 2) 22.5° 3) 50° 4) 35°

What is the correct measure of angle ∠DBC if ∠BAC is given as 45°?

Answer:

If ∠BAC = 45°, the measure of angle ∠DBC is 135°.

To find the measure of angle DBC, we need to use the property that the sum of the angles in a triangle is 180°. Since angle BAC is given as 45° and angle BAC and angle DBC are adjacent angles, they form a linear pair and together add up to 180°. Given that angle BAC is 45°, we can find the measure of angle DBC as follows:

Angle DBC = 180° - angle BAC

Angle DBC = 180° - 45°

Angle DBC = 135°

Therefore, the correct answer is 135°. Option 4) 35° is incorrect because it does not match the calculations.