In fig.6.14, line XY and MN interest at O. if angle POY=90° and a:b = 2:3.find c.
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Solution :
We know that the sum of linear pair are 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°
x = 90/5
So, x= 18°
a = 2.x 18° = 36°
Similarly b can be calculated and the value will be
b = 3 x 18° = 54°
From the diagram, b +c also forms a straight angle so,
b + c = 180°
c + 54° = 180°
c = 180° - 54°
c = 126°
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