### If lines XY and MN intersect as shown below and a:b = 1:2, find c.

**Answer:**

120°

**Step by Step Explanation:**

- As XY is a straight line, and the sum of the angles on a straight line is equal to 180°.

We have, a + b + 90° = 180°

⇒ a + b = 90°. - We may notice that the angles MOY and XON are vertically opposite angles.

So, a + 90° = c (vertically opposite angles are equal). - We are given a:b = 1:2, or

=a b

.1 2

Cross multiplying the fractions, we get,

2a = 1b. - We put b = 2a in a + b = 90° and get,

a + 2a = 90°, or 3a = 90°. Dividing each side by 3, we get,

a =

, or 30°.90° 3 - Now, since b = 2a.

We can say that b = 2 × 30°, or b = 60°. - From step 2, we have,

c = a + 90°, or c = 30° + 90°,

or c =**120°**.