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kompoz [17]
3 years ago
12

What is the exterior and interior angle of a 18 sided polygon

Mathematics
1 answer:
GREYUIT [131]3 years ago
3 0
Would assume the Polygon is an 18 sided regular polygon.

Exterior angle for regular polygon = 360/n      (Sum of angles of exterior angles = 360°)

where n = number of sides.

Exterior angle = 360 / 18 = 20

Exterior angle = 20°

Sum of exterior angle + Interior angle = 180°    (Both angles are on a straight line, so the sum is 180°)

Interior angle = 180° - 20°

Interior angle = <span>160°

</span>Hope this explains it.    
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OM , ON and OP are the angle bisectors of ∠AOB, ∠BOC, and ∠COD respectively. ∠AOD and ∠BOE are straight angles.
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Find m∠BOC, if m∠MOP = 110°.

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Step-by-step explanation:

A diagram has been drawn and attached below.

  • OM bisects AOB into angles x and x respectively
  • ON bisects ∠BOC into angles y and y respectively
  • OP bisects ∠COD into angles z and z respectively.

Since ∠AOD is a straight line

x+x+y+y+z+z=180 degrees

2x+2y+2z=180^\circ

We are given that:

m∠MOP = 110°.

From the diagram

∠MOP=x+2y+z

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x+2y+z=110°.

Solving simultaneously by subtraction

2x+2y+2z=180^\circ

x+2y+z=110°.

We obtain:

x+z=70°

Since we are required to find ∠BOC

∠BOC=2y

Therefore from x+2y+z=110° (since x+z=70°)

70+2y=110

2y=110-70

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Therefore:

m∠BOC= 40 degrees

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