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

120°

Step by Step Explanation:
1. 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°.
2. We may notice that the angles MOY and XON are vertically opposite angles.
So, a + 90° = c (vertically opposite angles are equal).
3. We are given a:b = 1:2, or
 a b
=
 1 2
.
Cross multiplying the fractions, we get,
2a = 1b.
4. We put b = 2a in a + b = 90° and get,
a + 2a = 90°, or 3a = 90°. Dividing each side by 3, we get,
a =
 90° 3
, or 30°.
5. Now, since b = 2a.
We can say that b = 2 × 30°, or b = 60°.
6. From step 2, we have,
c = a + 90°, or c = 30° + 90°,
or c = 120°.