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spin [16.1K]
3 years ago
6

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

Mathematics
1 answer:
qwelly [4]3 years ago
7 0

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 =\dfrac{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\times 42.29)^\circ

m\angle C=126.87^\circ

Therefore, the measure of angle C is 126.87 degrees.

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