From the following diagram;

What is the value of ∠LOY + ∠YOM + ∠XOM, if ∠XOl = 35°?

Option 1 : 325°

Concept Used:

A linear pair is a pair of adjacent angles formed when two lines intersect.

Formula used:

Sum of angles of linear pair = 180°

Calculation:

Here, ∠XOl = 35°

∠YOL and ∠XOL are linear pair

⇒ ∠YOL + ∠XOL = 180°

⇒ ∠YOL + 35° = 180°

⇒ ∠YOL = 180° - 35° = 145°

As, ∠XOI and ∠YOM is vertically opposite angles.

⇒ ∠XOl = ∠YOM = 35°

And, ∠YOM and ∠XOM are linear pair

⇒ ∠YOM + ∠XOM = 180°

⇒ 35° + ∠XOM = 180°

⇒ ∠XOM = 180° - 35° = 145°

Now, ∠YOL + ∠XOI + ∠XOM = 145° + 35° + 145° = 325°

∴ The value of **∠LOY + ∠YOM + ∠XOM is 325°.**