Is There A Regular Polygon Such That Each Exterior Angle Measures 75 Explain?

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What is the sum of the measures of the exterior angles of a regular polygon if each exterior angle measures 120? 360 degrees and the polygon is an equilateral triangle. How many sides would a regular polygon have if one of its exterior angles measures 51 degrees?

A regular polygon is one in which all the sides and angles are equal. The polygon with 8 equal sides is an octagon. The formula to find out the individual external angles of a polygon is given by, An exterior angle of a polygon = 360°/ Number of sides of the polygon.

is there a regular polygon such that each exterior angle measures 75 explain?

An exterior angle of a regular polygon measures 22.5°. How many sides does it have? 8. An interior angle of a regular polygon measures 170°. … 128°, 147º, and 130°. If the two remaining angles are equal in measure, what is the measure of each angle? 12. Find the value of x. 13. Find the value of x.

Explanation: What we are given is that there is a regular polygon with exterior angles that equal #120#degrees. Any exterior angle added to its interior angle is equal to #180#degrees because they make a straight angle. Knowing this, we can calculate the measure of the interior angles: #120 + x = 180#. #x = 60#.

Answer (1 of 8): Hi Kate, from your profile picture, you sound like a bright young girl, and I love your question. I would like to share with you a way to think about these problems. I hope it is helpful to you. Imagine yourself “walking” around a regular polygon.

Frequent Questions – 💬

❓ How do you find the exterior angles of a regular polygon?

Since the sum of exterior angles of any polygon is always equal to 360°, we can divide by the number of sides of the regular polygon to get the measure of the individual angles. Each exterior angle in a regular pentagon measures 72°. In the following table, we can see the exterior angle measures of some common regular polygons.

❓ Why is a regular polygon an equilateral triangle?

Solution: Since the polygon is regular, the measure of all the interior angles is the same. Therefore, all its exterior angles measure the same as well, that is, 120 degrees. Since the polygon has 3 exterior angles, it has 3 sides. Hence it is an equilateral triangle.

❓ What is the measure of one of the exterior angles?

We can see that all the exterior angles of a polygon have a total sum of 360°. Therefore, we can calculate the measure of one of the exterior angles of a regular polygon by dividing 360° by the number of sides of the regular polygon. For example, for a pentagon, we have: 360°÷5 = 72°

❓ How does the number of sides of a polygon affect its length?

This means that as number of sides of the polygon increase, the measures of the individual exterior angles get smaller. A regular polygon is a geometric figure that has all its sides with the same length and all its interior angles with the same measure. This means that all of its exterior angles also have the same measure.


⏯ – Exterior Angles of Polygons


⚡Popular questions on the topic: “is there a regular polygon such that each exterior angle measures 75 explain?”⚡

Is it possible to have a regular polygon with an exterior angle of 75?

No it is not possible
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Is it possible to have a regular polygon each of whose interior angle is 75 degree justify your answer?

Step-by-step explanation: It impossible for a interior angle of a regular polygon to equal degrees. … The sum of the exterior angles of any polygon is degrees, so the number of sides would be supposedly equal to or . A polygon cannot have sides, so the angle can't measure degrees.
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Is it possible to have a regular polygon with the measure of each exterior angle as 22 degree?

Since 22 is not a proper multiple of 360, the polygon wont be possible.
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Is it possible to have a regular polygon each of whose exterior angles is 70?

1 Expert Answer An exterior angle of a regular n-gon (a polygon with n sides) has a measure of 360/n. This means the measurement of an exterior angle of a regular polygon must be a factor of 360. So it is not possible that the measure of an exterior angle of a regular polygon is 70.
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How many sides does a regular polygon have if each exterior angle measures 72?

5 sidesWe do this by dividing 360° by the size of one exterior angle, which is 72°. The answer is 360° ÷ 72° = 5 sides.
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What is a regular polygon find the measure of exterior angle of a regular polygon of 15 sides?

Exterior angle=24 for polygon of 15 sides.
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Is it possible to have a regular polygon each of whose interior angle is 45o give reason?

No it is not possible to have a regular polygon each of whose interior angle is 45°. Let the side be n. number. so,it is not possible to have a regular polygon each of whose interior angle is 45°.
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Is it possible to have a regular polygon whose each interior angle is 105⁰?

Solution. Therefore, no polygon is possible whose each interior angle is 105°.
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Is it possible to have a regular polygon each of whose exterior angle is 80 degree?

Hence it is not possible to have a regular polygon whose each exterior angle is of 80°.
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Is it possible to have a regular polygon whose each exterior angle measures 35 Justify your answer?

it is not possible to have such a regular polygon . Thus we conclude that, this statement is false .. The exterior angle and the adjacent angle in a regular polygon is supplementary .
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Is it possible to have a regular polygon each of whose exterior angle is 50⁰?

1 Answer. Rimo · Stefan V. No, you cannot make a regular polygon with each exterior angle of 50∘ .
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What polygon has exterior angles of 72?

The Regular Polygon with Exterior Angles of 72o is a Pentagon.
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Can you draw a regular polygon with exterior angles of 72 degrees?

Answer: If the exterior angle of a regular polygon is 72 degrees, then the polygon has 360/72 = 5 sides or is a regular pentagon.
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In which regular polygon is the measure of interior angle equal to the measure of exterior angle?

Solution: Since the polygon is regular, the measure of all the interior angles is the same. Therefore, all its exterior angles measure the same as well, that is, 120 degrees….Exterior Angles Examples.

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What is the number of sides of a regular polygon if each exterior angle measure 180?

The answer is 180° – 72° = 108°. (b) Calculate the number of sides in the regular polygon. We do this by dividing 360° by the size of one exterior angle, which is 72°. The answer is 360° ÷ 72° = 5 sides….Question 2.

(a) a regular decagonexterior = °
interior = °
(b) a regular pentagonexterior = °
interior = °

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What is the number of sides of a regular polygon whose each exterior angle has a measure of 45?

8The correct option is A 8 The regular polygon whose each exterior angle has a measure of 45 degrees, has __ sides.
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Is it possible to have a regular polygon whose each interior angle is?

Hence, it is possible to have a regular polygon whose interiro angle is 135° . Hence, it is possible to have a regular polygon whose interior angle is 138°.
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Is it possible to have a regular polygon with each interior angle equal to 105o explain showing steps?

Solution. Therefore, no polygon is possible whose each interior angle is 105°.
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Is it possible to have a regular polygon each of whose exterior angles is 45 degree?

Given that Exterior angle = 45° Let number of sides = n In a regular Polygon Sum of the exterior angles = 360° Exterior Angle × Number of sides = 360° 45° × n = 360° n = 360"°" /45"°" n = 8 ∴ Polygon has 8 Sides.
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Is it possible to have a regular polygon whose each exterior angle is 40 of a right angle?

Hence it is possible to have a regular polygon whose exterior angle is 40% of the right angle.
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⏯ – Exterior angles of regular polygons and exterior and interior angle relationship


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