Question

The angles of a heptagon are as follows: x, x + 20, x + 30, x + 40, x − 10, x + 70, x − 20 Find the measure of each angle of the heptagon.

Answer 1

Here's the answer for your question:

x = 110°

x+20 = 130°

x+30 = 140°

x+40 = 150°

x-10 = 100°

x+70 = 180°

x-20 = 90°

Here's step by step explanation:

The sum of all the angles in a Heptagon is equal to 900°.

According to the question:-

The angles are:-

1. x
2. (x+20)
3. (x+30)
4. (x+40)
5. (x-10)
6. (x+70)
7. (x-20)

So,

The equation becomes,

[x+(x+20)+(x+30)+(x+40)+(x-10)+(x+70)+(x-20)]° = 900°

x+x+20+x+30+x+40+x-10+x+70+x-20 = 900°

7x° + 130° = 900°

7x° = 900°-130°

7x° = 770°

x° = 110°

So,

The angles will be

1. x = 110°
2. (x+20) = 130°
3. (x+30) = 140°
4. (x+40) = 150°
5. (x-10) = 100°
6. (x+70) = 180°
7. (x-20) = 90°

Hope u understood.