Determine the value of x for the diagram shown.
A) 30
B) 45
C) 60
D) 80

Answer:
Option C. 60°
Step-by-step explanation:
In the triangle ABC,
AC ≅ BC
Therefore, angles opposite to these sides will be equal.
∠A ≅ ∠C ≅ x°
and ∠ ACB + ∠ACD = 180° [Supplementary angles]
∠ACB + 120° = 180°
∠ACB = 180 - 120 = 60°
Now ∠A + ∠B + ∠ACB = 180°
x + x + 60 = 180
2x + 60 = 180
2x = 180 - 60
2x = 120
x = [tex]\frac{120}{2}[/tex]
x = 60°
Option C. is the answer.