Question

2. In Fig. 6.14, lines XY and MN intersect at O. If
POY = 90° and a : b= 2:3, find c.

Answer 1

Step-by-step explanation:

Let ∠ a = 2x, then ∠b = 3x

(sum of angle in linear pair always equal to 180° )

∠XOM + ∠MOP + ∠POY = 180°

∠b + ∠a + ∠POY = 180°

given that ∠POY = 90°

plug this value we get

3x + 2x + 90° = 180°

5x = 90°

x = 18°

a = 2x = 2 × 18 = 36°

b = 3x = 3 ×18 = 54°

MN is a straight line.

sum of angle in linear pair always equal to 180°

so that ∠b + ∠c = 180°

54° + ∠c = 180°

∠c = 180° − 54° = 126°

∠ c = 126°

Answer 2

Step-by-step explanation:

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sum of linear pair = 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°

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