Question

$\displaystyle\huge\red{\underline{\underline{Solution}}}$
$\bold\pink{find \: the \: value \: of \: x}...............$
​

Answer 1

________________________

★ Sᴏʟᴜᴛɪᴏɴ :-

By observing the given figure

• There is a straight line QOR = 180°
• There are two angles = 5x , 3x

Now , finding x using straight line property

Straight line property :- Sum of all angles on a straight line is always equal to 180°

Here , the angles on straight line are 5x & 3x

∠QOP + ∠POR = 180°

⇒ 5x + 3x = 180°

⇒ 8x = 180°

⇒ x = 180° ÷ 8

⇒ x = 22.5°

∴ Hence , x = 22.5°

_______________________

★ Vᴇʀɪꜰɪᴄᴀᴛɪᴏɴ :-

By substituting the value of x , we can verify that the answer is correct

• 5x + 3x = 180°

Taking LHS & substituting the value of x

➸ 5(22.5) + 3(22.5)

➸ 112.5 + 67.5

➸ 180°

By comparing with RHS

LHS = RHS

∴ Hence , verified

_______________________

Answer 2

Answer:

Given QR is a Line, Hence it will be 180° at Point O.

• According to the Question :

⇒ ∠ QOP + ∠ ROP = 180°

⇒ 5x + 3x = 180°

⇒ 8x = 180°

• Dividing both by 8

⇒ x = 22.5°

∴ Hence, the required value of x is 22.5°

⠀⠀⠀⠀⠀───────────────

• Required Angles :

◗ 5x = 5(22.5°) = 112.5°

◗ 3x = 3(22.5°) = 67.5°