Question

The sum of the angles in a hexagon is 720°.

a. Write an equation that can be used to determine the value of x.
b. Solve your equation algebraically
c. Determine the measure of angle c.

Answer 1

Given:

The sum of the angles in a hexagon is 720°.

`m\angle A=90^\circ,m\angle B=126.87^\circ,m\angle C=(3x)^\circ,m\angle D=90^\circ, m\angle E=143.13^\circ, m\angle F=143.13^\circ.`

To find:

(a) Equation to solve the value of x.

(b) The value of x.

(c) The measure of angle C.

Solution:

(a)

We have,

`m\angle A=90^\circ,m\angle B=126.87^\circ,m\angle C=(3x)^\circ,m\angle D=90^\circ, m\angle E=143.13^\circ, m\angle F=143.13^\circ.`

The sum of the angles in a hexagon is 720°.

`m\angle A+m\angle B+m\angle C+m\angle D+m\angle E+m\angle F =270^\circ`

`90^\circ+126.87^\circ+(3x)^\circ+90^\circ+143.13^\circ+143.13^\circ =270^\circ`

`90+126.87+(3x)+90+143.13+143.13 =720`

Therefore, the required equation is
`90+126.87+(3x)+90+143.13+143.13 =720`.

(b)

On solving the above equation, we get

`593.13+3x =720`

`3x =720-593.13`

`3x =126.87`

Divide both sides by 3.

`x =(126.87)/(3)`

`x =42.29`

Therefore, the value of x is 42.29.

(c)

We need to find the measure of angle C.

`m\angle C=(3x)^\circ`

`m\angle C=(3* 42.29)^\circ`

`m\angle C=126.87^\circ`

Therefore, the measure of angle C is 126.87 degrees.