Question

I need help on this. Anyone know the answer?

Answer 1

Given

• Angles of polygons

To Find

• Value of x

We know that

• The sum of all exterior angles of a polygon is 360°.

${\therefore \sf (78) + (2x + 13) + (3x - 9) + (x + 5) + (x + 14) + (x + 11) = 360}$

${\implies \sf 78 + 2x + 13 + 3x - 9+ x + 5 + x + 14+ x + 11 = 360}$

${\implies \sf 8x + 112 = 360}$

• Subtracting both sides by 112

${\implies \sf 8x + 112 - 112 = 360 - 112}$

${\implies \sf 8x = 248}$

• Dividing both sides by 8

${\implies \sf \dfrac{8x}{8} = \dfrac{248}{8} }$

${ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf x = 31 }$

$\: \: \: \: \: \: \: \: \underline{{ \text{Hance \: the \: value \: of \: x \: is \: 31°}.}}$