Answer
x = 15
Step-by-step explanation
Given:
The given shape (heptagon) has 7 sides and 7 angles.
what to find;
The value of x.
Step-by-step solution:
To solve for x, use the sum of angles of heptagon = (n - 2)180
Put n = 7 into the formula
(7 - 2)180
5 x 180 = 900⁰
The sum of the angles of the heptagon = 900⁰
∴ (7x + 1) + 10x + (6x + 7) + (10x - 9) + (9x + 4) + (8x + 10) + (9x + 2) = 900⁰
Rearrange and group the terms.
7x + 10x + 6x + 10x + 9x + 8x + 9x + 1 + 7 - 9 + 4 + 10 + 2 = 900⁰
59x + 15 = 900⁰
59x = 900 - 15
59x = 885
Divide both sides by 59
59x/59 = 885/59
x = 15