Question

the sides of a pentagon are produced in order and the exterior angle should obtain , measure x° , 2x° and 3x + 10° and 4x + 5° and 5x°, find x and measure of each exterior angle of pentagon?

Answer 1

Given :

• Measure of exterior angles of Pentagon :

1. (x)°
2. (2x)°
3. (3x + 10)°
4. (4x + 5)°
5. (5x)°

To find :

• Value of x
• Measure of each angle of Pentagon

Solution :

✯ Sum of all the exterior angles of a Pentagon = 360° ✯

• x + 2x + 3x + 10 + 4x + 5 + 5x  360

• 15 x + 15 = 360
• 15x = 360 - 15
• x = ³⁴⁵⁄₁₅
• x = 23

★ The value of x is 23° ★

Measure of each angle :

• x° = 23°
• (3x)° = 3 × 23 = 46°
• (4x + 5)° = 4 × 23 + 5 = 97°
• (3x + 10)° = 3 × 23 + 10 = 79°
• (5x)° = 5 × 23 = 115°

Verification :

• (x)° + (2x)° + (3x + 10)° + (4x + 5)° + (5x°) = 360°
• 23° + 46° + 97° + 79° + 115° = 360°
• 360° = 360°

Answer 2

Answer:

x° = 23°

(3x)° = 3 × 23 = 46°

(4x + 5)° = 4 × 23 + 5 = 97°

(3x + 10)° = 3 × 23 + 10 = 79°

(5x)° = 5 × 23 = 115°

Step-by-step explanation: