In the given figure, what is the value (in degrees) of x + y + z?
Show answer & explanation
Correct answer: A
Explanation
Given:
Exterior angle at C on AC = 105°
Exterior angle at D = 125°
According to the formulas:
Sum of angles on a straight line = 180°
Sum of the three angles of a triangle = 180°
∠ACB (Interior angle of triangle ABC) = 180 − 105 = 75°
In triangle ACD:
∠ADC = 180 − 125 = 55°
∠ACD = 105°
Therefore, ∠CAD (y) = 180 − (105 + 55) = 20°
In triangle ABC:
x + z + 75 = 180
x + z = 105
Therefore:
x + y + z = 105 + 20 = 125°