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

Given:

• XY and MN intersect each other at O
• POY = 90°
• a : b = 2:3

To Find:

• Find C?

Solution:

We know that,

$\circ{\underline{\boxed{\sf{ \green{ Sum \ of \ Angles_{(Linear \ Pair )} } = 180° }}}}$

So,

$\colon\implies$ POY + a + b = 180°

Putting the value;

$\colon\implies$POY + a + b = 180

$\colon\implies$ 90 + a + b = 180°

$\colon\implies$ a + b = 180° - 90°

$\colon\implies$ a + b = 90°

Now,

• a : b = 2 : 3

Let a be 2x and b be 3x

∴ 2x + 3x = 90°

After solving Equation,

$\colon\implies$ 5x = 90°

$\colon\implies$ ${\tt{ x = \cancel{ \dfrac{90}{5} } }}$

$\colon\implies$ x = 18°

$\circ \: \: \: {\boxed{\tt\orange{ a = 2 \times 18° = 36° }}}$

$\circ \: \: \: {\boxed{\tt\purple{b = 3 \times 18° = 54° }}}$

From the diagram, (b + c) also forms a straight angle so,

$\colon\implies$ b + c = 180°

$\colon\implies$ c + 54° = 180°

$\colon\implies$ c = 126°

Hence,

• The value of the c is 126°.

Answer 2

Step-by-step explanation:

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°