Question

Find the value of x in the polygon below (Image available)

Answer 1

Answer :-

• Value of x is 100°

Given :-

• A polygon.

To Find :-

• Value of x

Solution :-

Here, angles are

• 148°
• (x + 23)°
• 92°
• 135°
• 122°
• x°

As we know that

Sum of all angles of a hexagon is 720°

According to question :-

148 + (x + 23) + 92 + 135 + 122 + x = 720

⇒ 148 + x + 23 + 92 + 135 + 122 + x = 720

⇒ 148 + 23 + 92 + 135 + 122 + x + x = 720

⇒ 263 + 135 + 122 + 2x = 720

⇒ 520 + 2x = 720

⇒ 2x = 720 - 520

⇒ 2x = 200

⇒ x = 200/2

⇒ x = 100

Hence,

• Value of x = 100°
• Value of (x + 23) = 100 + 23 = 123°

Answer 2

Given :-

A polygon.

To Find :-

Value of x

Solution :-

Here, angles are

• 148°
• (x + 23)°
• 92°
• 135°
• 122°
• x°

As we know that

Sum of all angles of a hexagon is 720°

According to question :-

148 + (x + 23) + 92 + 135 + 122 + x = 720

⇒ 148 + x + 23 + 92 + 135 + 122 + x = 720

⇒ 148 + 23 + 92 + 135 + 122 + x + x = 720

⇒ 263 + 135 + 122 + 2x = 720

⇒ 520 + 2x = 720

⇒ 2x = 720 - 520

⇒ 2x = 200

⇒ x = 200/2

⇒ x = 100

Hence,

Value of x = 100°

Value of (x + 23) = 100 + 23 = 123°