In the given figure, MN ∥ AB, ∠OMN = 110°, and ∠OAC = 30°. What is the value of ∠OCA?

Option 4 : 40°

**Given:**

MN ∥ AB, ∠OMN = 110°, and ∠OAC = 30°

Concept:

The Sum of all the angles of the triangle is 180°

Parallel lines are lines that are lying on the same plane but will never meet

When a transversal line cuts two lines, the properties below will help us determine whether the lines are parallel.

The properties below will help us determine and show that two lines are parallel.

1. Corresponding angles are equal

b = f, a = e, d = h and c = g

2. Alternate interior angles are equal.

c = f and d = e

3. Alternate exterior angles are equal.

a = h and b = g

4. Consecutive interior angles add up to 180°.

c + e = 180° and d + f = 180°

5. Consecutive exterior angles add up to 180°

**Calculation:**

Corresponding angles are equal

∠OMN = ∠COA = 110°

In ΔOAC

∠COA + ∠OCA + ∠OAC = 180°

⇒ 110° + ∠OCA + 30° = 180°

⇒ ∠OCA = 40°