Question

The exterior angles of a heptagon are x, 2x + 5, 3x + 15, 7x – 5, 8x – 10, 6x – 20 and 3x. Find the value of x.

Also find the measure of each of its exterior & interior angle.​

Answer 1

Answer:

As given below

Step-by-step explanation:

Given data exterior angles of a heptagon are

             x°, (2x+5)°, (3x+15)°, (7x-5)°, (8x -10)°, (6x - 20)°, (3x)°  

⇒ We know that heptagon has 7 sides

⇒ sum of the exterior angles in a polygon = 360°

⇒ x+ 2x + 5 + 3x + 15 + 7x - 5 + 8x -10 +6x -20 + 3x = 360°

⇒   30x + 15 - 30 = 360°

⇒  30x -15 = 360°

⇒  30 x = 375

⇒  6 x = 75

⇒  x = 12.5  

⇒ exterior angles are

⇒ x = 12.5°  ,                                

⇒ 2x + 5 = 2(12.5) +5 = 25 + 5 =30°

⇒ 3x + 15 = 3(12.5) +15 = 37.5 +15 =52.5°

⇒ 7x -5 = 7 (12.5) - 5 = 87.5 -5 = 82.5°

⇒ 8x -10 = 8(12.5) - 10 = 100 - 10 = 90°

⇒ 6x -20 = 6(12.5) -20 = 75 -20 = 55°  

⇒ 3x = 3 (12.5) = 37.5°  

⇒ interior angles are

⇒ in a polygon exterior angle + interior angle = 180°

⇒ interior angle = 180° - exterior angle

⇒ interior angles at given exterior angles

at 12.5°  = 180° - 12.5° = 167.5°  

at 30°  = 180° - 30° = 150°

at 52.5° = 180° - 52.5° = 127.5°

at 82.5° = 180° - 82.5° = 97.5°

at 90°  =  180° - 90° = 90°

at 55° = 180° - 55° = 125°

at 37.5° = 180° - 37.5° = 142.5°