Angles Of Polygons

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| By Yonghs
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Yonghs
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Quizzes Created: 2 | Total Attempts: 2,914
| Attempts: 1,940
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  • 1/10 Questions

    Each exterior angle of a regular nonagon is

    • 20Ëš
    • 40Ëš
    • 50Ëš
    • 60Ëš
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About This Quiz

Sum of exterior angles = 360

sum of interior angles = (n-2)180
where n = no. Of sides

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  • 2. 

    Each interior angle of a regular hexagon is

    • 60Ëš

    • 120Ëš

    • 180Ëš

    • 240Ëš

    Correct Answer
    A. 120Ëš
    Explanation
    A regular hexagon has six sides that are all equal in length and six angles that are all equal in measure. To find the measure of each interior angle, we can use the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, n is 6, so (6-2) * 180 = 4 * 180 = 720. Since all angles are equal, we divide 720 by 6 to find that each interior angle is 120Ëš.

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  • 3. 

    An octagon has interior angles that measure 158Ëš, 115Ëš, 123Ëš, 149Ëš, (x +5) Ëš, (2x – 59) Ëš, (x +15) Ëš and (x +24) Ëš. Find the value of x.

    • 155

    • 110

    • 200

    • 220

    Correct Answer
    A. 110
    Explanation
    The sum of all interior angles in an octagon is equal to 1080 degrees. We can set up an equation to find the value of x by adding up all the given angles and setting it equal to 1080. By simplifying the equation, we can solve for x and find that x is equal to 110.

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  • 4. 

    ABCDEFGHI is a regular polygon. Angle ABC measures

    • 40Ëš

    • 80Ëš

    • 140Ëš

    • 160Ëš

    Correct Answer
    A. 140Ëš
    Explanation
    The answer is 140Ëš because in a regular polygon, all angles are equal. Since the sum of all angles in a polygon is equal to (n-2) * 180Ëš, where n is the number of sides, we can calculate the measure of each angle by dividing the sum by the number of sides. In this case, if we assume that the polygon has 9 sides, the sum of all angles would be (9-2) * 180Ëš = 1260Ëš. Dividing this sum by 9, we get 140Ëš for each angle.

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  • 5. 

    In a regular polygon, each exterior angle measures 24 degrees. How many sides does the polygon have?

    • 12

    • 15

    • 18

    • 24

    Correct Answer
    A. 15
  • 6. 

    ABCDE is a regular polygon. Angle ABC measures

    • 36Ëš

    • 72Ëš

    • 108Ëš

    • 144Ëš

    Correct Answer
    A. 108Ëš
    Explanation
    A regular pentagon has 5 equal sides and 5 equal interior angles. To find the measure of each angle, you need to know that the sum of the interior angles of a pentagon is 540 degrees. Divide this sum by the number of angles (5) to find the measure of each angle: 540° / 5 = 108°. Therefore, angle ABC in a regular pentagon measures 108 degrees.

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  • 7. 

    A k-sided polygon has interior angles that measure 145, 157, (x+15), (2x-58), (x+18), (x-11), x and 178 degrees. Find the value of x. 

    • 106

    • 127.2

    • 166

    • 212

    Correct Answer
    A. 106
    Explanation
    Since the sum of the interior angles of a k-sided polygon is given by the formula (k-2) * 180 degrees, we can set up the equation (k-2) * 180 = 145 + 157 + (x+15) + (2x-58) + (x+18) + (x-11) + x + 178. Simplifying the equation gives us 180k - 360 = 540 + 6x. Rearranging the equation further, we get 6x = 180k - 900. Since both x and k are integers, we can see that the value of x must be a multiple of 6. The only answer choice that satisfies this condition is 106, so it is the correct answer.

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  • 8. 

    A k-sided polygon has 3 interior angles measuring 145, 157 and 178 degrees; and the remaining angles measure 150 degrees each. Find the value of k. 

    • 10

    • 11

    • 13

    • 15

    Correct Answer
    A. 13
    Explanation
    A k-sided polygon has k interior angles. In this case, we are given that three of the interior angles measure 145, 157, and 178 degrees. We are also told that the remaining angles measure 150 degrees each. To find the value of k, we need to determine how many angles measure 150 degrees. Since the sum of the interior angles in a polygon is given by (k-2) * 180 degrees, we can set up the equation (k-2) * 180 = 145 + 157 + 178 + (k-3) * 150. Simplifying this equation, we find that k = 13. Therefore, the value of k is 13.

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  • 9. 

    A nonagon has 3 interior angles that measure 158Ëš, 115Ëš, 123Ëš; and the remaining angles are each equal to (x +15) Ëš. Find the value of x.

    • 129

    • 144

    • 159

    • 216

    Correct Answer
    A. 129
    Explanation
    The sum of the interior angles of a nonagon is given by the formula (n-2) * 180, where n is the number of sides of the polygon. In this case, n=9, so the sum of the interior angles is (9-2) * 180 = 7 * 180 = 1260Ëš.

    We are given that three of the interior angles measure 158Ëš, 115Ëš, and 123Ëš. To find the value of x, we subtract the sum of these three angles from the total sum of the interior angles: 1260Ëš - (158Ëš + 115Ëš + 123Ëš) = 864Ëš.

    Since the remaining angles are each equal to (x + 15)Ëš, we can set up the equation 3(x + 15) = 864Ëš. Solving for x gives us x = 129.

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  • 10. 

    ABCDE is a regular polygon. Angle ACD measures

    • 36Ëš

    • 72Ëš

    • 108Ëš

    • 144Ëš

    Correct Answer
    A. 72Ëš
    Explanation
    A regular hexagon has 6 equal sides and 6 equal interior angles. To find the measure of each interior angle, you can use the formula: (n-2) * 180° / n, where 'n' is the number of sides. For a hexagon, this is (6-2) * 180° / 6 = 120°.
    However, the question asks for angle ACD, which is not an interior angle. To find this, we need to draw a diagonal from A to C, creating an isosceles triangle ABC. Each base angle of this triangle (angles BAC and BCA) measures half the difference between the interior angle and 180°: (120° - 180°) / 2 = 30°.
    Since the angles in a triangle add up to 180°, angle ACD is 180° - 30° - 30° = 120°. Finally, we divide this by 2 to find the measure of angle ACD: 120° / 2 = 72°.

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  • Current Version
  • Oct 15, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Sep 03, 2009
    Quiz Created by
    Yonghs
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