In the given figure, angle ABC = 65 degrees and angle ACD = 120 degrees.
What is the value (in degrees) of angle BAC?

Correct option is C

Given:

∠ABC = 65°

∠ACD = 120°

Find ∠BAC

Concept Used:

Exterior angle property

Sum of angles in a triangle

Formula Used:
Interior angle + exterior angle = 180°
Sum of angles of a triangle = 180°

Solution:

Since B, C, and D are on a straight line:

∠ACB = 180° − 120° = 60°

Now in triangle ABC:

∠BAC + ∠ABC + ∠ACB = 180°

∠BAC + 65° + 60° = 180°

∠BAC = 180° − 125°

∠BAC = 55°

Therefore,

∠BAC = 55°