Question

Value of ∠Y in the following figure is _______

• A. ${120}^{\circ }$
• B. ${80}^{\circ }$
• C. ${140}^{\circ }$
• D. ${85}^{\circ }$

Answer 1

The correct option is B ${80}^{\circ }$


In the figure, ∠BCA and ∠ACE are linear pair.

So, ∠BCA + ∠ACE = 180°
⇒ 120° + ∠X = 180°
⇒ ∠X = 180° - 120° = 60°

Angle sum property of a triangle tells that the sum of the measures of the three internal angles of the triangle is 180°.

From △DCE, we have:
60° + ∠Y + 40° = 180°
⇒ ∠Y = 180° - 100° = 80°