In the given figure, what is the value (in degrees) of (x+y+z)?
Show answer & explanation
Correct answer: C
Explanation
Given:
∠ACD = 105°
∠CDA = 140°
According to the formulas:
Exterior Angle Theorem of a triangle and Sum of angles in a triangle = 180°
∠ADC = 180° − 140° = 40°
In triangle ACD:
y + 105° + 40° = 180°
y = 180° − 145° = 35°
Straight line at point C:
∠ACB = 180° − 105° = 75°
In triangle ABC:
x + z + 75° = 180°
x + z = 105°
Therefore:
x + y + z = 105° + 35° = 140°