Question

8. Find the value of x in the following figure:
+ 59°
2
4​

Answer 1

Answer:

• The value of x is 172°.

Step-by-step explanation:

We know that:

• Sum of all the angles around a point is 360°.

To Find:

• The value of x.

Finding the value of x:

According to the question.

⇒ x/2 + 59° + x/4 + x = 360°

⇒ x/2 + x/4 + x = 360° - 59°

⇒ (2x + x + 4x)/4 = 301°

⇒ 7x/4 = 301°

Cross multiplication.

⇒ 7x = 301° × 4

⇒ 7x = 1204°

⇒ x = 1204°/7

⇒ x = 172°

∴ The value of x = 172°

Answer 2

We know that, sum of all angles around a point is 360°.

⠀⠀ ━━━━━━━━━━━━━━━━━━━━━━

⠀

$\sf{\underline{According\: to\: the\: question}}$

⠀

$\sf{\dashrightarrow{\dfrac{x}{2} + 59^{\circ} + \dfrac{x}{4} + x = 360^{\circ}}}$

⠀

$\sf{\dashrightarrow{\dfrac{x}{2} + \dfrac{x}{4} + x = 360^{\circ} - 59^{\circ}}}$

⠀

$\sf{\dashrightarrow{\dfrac{2x + x + 4x}{4} = 301^{\circ}}}$

⠀

$\sf{\dashrightarrow{\dfrac{7x}{4} = 301^{\circ}}}$

⠀

$\sf{\dashrightarrow{7x = 301^{\circ} \times 4}}$

⠀

$\sf{\dashrightarrow{7x = 1204^{\circ}}}$

⠀

$\sf{\dashrightarrow{x = \dfrac{1204^{\circ}}{7}}}$

⠀

$\mathfrak{\dashrightarrow{\boxed{\pink{x = 172^{\circ}}}}}$

⠀

Hence,

• The value of x is 172°.