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2 years ago

In a regular polygon each interior angle is 140° greater than each exterior angle. Calculate the number of sides of the polygon

Mathematics

1 answer:

pochemuha2 years ago

6 0

Answer:

18 sides.

Step-by-step explanation:

The interior and exterior angles sum to 180 so:

I + E = 180

also I - E = 140 (given)

So, adding to eliminate E:

2I = 320

I = 160 degrees and the external angle E = 1809 - 160 = 20 degrees.

Since the sum of all exterior angles in a polygon = 360 degrees

- the number of sides = 360 / 20 = 18.

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A 10 ft pole has a support rope that extends from the top of the pole to the ground. The rope and the ground form a 30 degree an

mr Goodwill [35]

Answer:

The length of rope is 20.0 ft . Hence, <u>option (1) </u> is correct.

Step-by-step explanation:

In the figure below AB represents pole having height 10 ft and AC represents the rope that is from the top of pole to the ground. BC represent the ground distance from base of tower to the rope.

The rope and the ground form a 30 degree angle that is the angle between BC and AC is 30°.

In right angled triangle ABC with right angle at B.

Since we have to find the length of rope that is the value of side AC.

Using trigonometric ratios

$\sin C=\frac{\text{perpendicular}}{\text{hypotenuse}}$

$\sin C=\frac{AB}{AC}$

Putting values,

$\sin 30^\circ} =\frac{10}{AC}$

We know, $\sin 30^\circ}=\frac{1}{2}$

$\frac{1}{2} =\frac{10}{AC}$

On solving we get,

AC= 20.0 ft

Thus, the length of rope is 20.0 ft

Hence, <u>option (1)</u> is correct.

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2 years ago

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mestny [16]

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Step-by-step explanation:

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2 years ago

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3 years ago

A wooden board has a volume of 0.225 cubic m and a mass of 146.25 kilograms.

Triss [41]

Answer:

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Step-by-step explanation:

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3 years ago

Help picture below problem 16

Allisa [31]

Answer:

Step-by-step explanation:

a²+b²=c²

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a²+12²=13³

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169-144=25

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2 years ago

In a regular polygon each interior angle is 140° greater than each exterior angle. Calculate the number of sides of the polygon​

In a regular polygon each interior angle is 140° greater than each exterior angle. Calculate the number of sides of the polygon