Question

In Figure, lines XY and MN intersect at O. If $∠$POY=90° and a:b=2:3, find c.

Answer 1

Given: $∠$POY= 90° and a: b = 2: 3.

Let the common ratio between a and b be x.
∴ XY is a straight line, rays OM and OP stand on it.
∴$∠$POY = $∠$POX = 90°
$∠$POX = ∠POM + $∠$MOX
90° = a + b
Now, a = 2x and b = 3x
$⇒$a + b = 90°
2x + 3x = 90°
5x = 90°
x = $\frac{90°}{5}$ = 18°
a = 2x = 2 $×$ 18°
a = 36°
b = 3x = 3 × 18°
b = 54°
Also, $∠$MOY= $∠$MOP + $∠$POY
= a + 90°
= 36° + 90° = 126°
∴ c = 126º