Question

In the given figure, I for what value of x will POQ be a straight line? ​

Answer 1

Answer:

Since the sum of angles on one side of a straight line = 180°, therefore...

2x + (3x + 30°) = 180° (straight line)

2x + 3x + 30° = 180°

5x + 30° = 180°

5x = 180° - 30°

5x = 150°

x = 150°/5

x = 30°.

Thus x = 30°.

Hope it helps! :)

Answer 2

• Value of x is 30°.

Step-by-step explanation:

To find:-

• Value of x.

Solution:-

Given that,

POQ is a straight line.

• Straight line always forms 180°.

We know,

Sum of all angles forms on straight line is equal to 180°. We can also say this statement $\blue { \sf \bold{Linear \: pair}}.$

So,

$\sf \longrightarrow \angle ROP + \angle ROQ = 180\degree$

$\sf \longrightarrow 2x + 3x + 30\degree = 180\degree$

$\sf \longrightarrow 5x + 30\degree = 180\degree$

$\sf \longrightarrow 5x = 180\degree - 30\degree$

$\sf \longrightarrow 5x = 150\degree$

$\sf \longrightarrow x = \dfrac{150\degree}{5}$

$\longrightarrow \purple{\boxed{\sf \bold{x=30 \degree}} \star}$

Verification:-

$\sf \longrightarrow \angle ROP + \angle ROQ = 180\degree$

$\sf \longrightarrow 2x + 3x + 30\degree = 180\degree$

• $\sf Put \: x = 30\degree$

$\sf \longrightarrow 2 \times 30\degree + 3 \times 30\degree + 30\degree = 180\degree$

$\sf \longrightarrow 60\degree + 90\degree + 30 \degree = 180\degree$

$\sf \longrightarrow 180\degree = 180\degree$

$\boxed{\sf Hence\: Verified.}$

Therefore,

Value of x is 30°.

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