Question

A convex hexagon's six interior angles are as follows: x°. x°, (2x - 3)°, (3x +7)°, (7x - 12)° and (6x +28)°. Solve for x.

A. 35
B. 37
C. 53
D. 55

Answer 1

The correct answer is B. 37. The sum of the interior angles of a convex hexagon are (6x +28)° + (7x - 12)° + (3x +7)° + (2x - 3)° + x° + x° = 720°. Solving for x gives x = 37.

Answer 2

35⁰

To solve for x, we need to find the sum of the interior angles of the hexagon and equate it to the known sum for a convex hexagon, which is 720°.

The sum of the interior angles is:

x° + x° + (2x - 3)° + (3x + 7)° + (7x - 12)° + (6x + 28)° = 720°

Expanding:

20x + 20 = 720

Subtracting 20 from both sides:

20x = 700

Dividing both sides by 20:

x = 35

So the value of x is 35.