Given:
The sum of the angles in a hexagon is 720°.
[tex]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.[/tex]
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,
[tex]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.[/tex]
The sum of the angles in a hexagon is 720°.
[tex]m\angle A+m\angle B+m\angle C+m\angle D+m\angle E+m\angle F =270^\circ[/tex]
[tex]90^\circ+126.87^\circ+(3x)^\circ+90^\circ+143.13^\circ+143.13^\circ =270^\circ[/tex]
[tex]90+126.87+(3x)+90+143.13+143.13 =720[/tex]
Therefore, the required equation is [tex]90+126.87+(3x)+90+143.13+143.13 =720[/tex].
(b)
On solving the above equation, we get
[tex]593.13+3x =720[/tex]
[tex]3x =720-593.13[/tex]
[tex]3x =126.87[/tex]
Divide both sides by 3.
[tex]x =\dfrac{126.87}{3}[/tex]
[tex]x =42.29[/tex]
Therefore, the value of x is 42.29.
(c)
We need to find the measure of angle C.
[tex]m\angle C=(3x)^\circ[/tex]
[tex]m\angle C=(3\times 42.29)^\circ[/tex]
[tex]m\angle C=126.87^\circ[/tex]
Therefore, the measure of angle C is 126.87 degrees.
