In: Math
In figure lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.
We know that the sum of linear pair is always equal to 180°
So,
∠POY +a +b = 180°
Putting the value of ∠POY = 90° (as given in the question) we get,
a+b = 90°
Now, it is given that a : b = 2 : 3 so,
Let a be 2x and b be 3x
∴ 2x+3x = 90°
Solving this we get
5x = 90°
So, x = 18°
∴ a = 2×18° = 36°
Similarly, b can be calculated and the value will be
b = 3×18° = 54°
From the diagram, b+c also forms a straight angle so,
b+c = 180°
c+54° = 180°
∴ c = 126°
The value of c is 126°.