Mathematics Questions and Answers – Sum of Measures of the Exterior Angles of a Polygon

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This set of Mathematics Exam Questions and Answers for Class 8 focuses on “Sum of Measures of the Exterior Angles of a Polygon”.

1. What are exterior angles of any polygon?
a) All angles within the polygon
b) The angles with measure as 90°
c) The angles forming a pair of supplementary angles
d) The angles forming a pair of complementary angles
View Answer

Answer: c
Explanation: If an extended ray along a side of a polygon form a linear pair with the same side of the polygon then the angle made by the polygon and the extended ray is said to be exterior angle of that polygon. Any polygon having ‘n’ number of sides the sum of all external angels is 360°.
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2. The sum total of all the external angles is always ________
a) (n-2)180°
b) 180°
c) (n-2)360°
d) 360°
View Answer

Answer: d
Explanation: As we know that the external angles for a supplementary pair of angles with the internal angles. We take any square of any length, as we know that all the angles of a square measure 90° and we also know that they are supplementary.
Therefore 90°+x = 180°
Therefore x = 90°
Similarly the other three external angles also measure the same. Therefore the sum total of all the external angles is 360°.

3. If perimeter of a rectangle is 24 m, then what would be the measure of each of the external angle of that rectangle?
a) 90°
b) 180°
c) 360°
d) 45°
View Answer

Answer: a
Explanation: We know that the rectangle has all it’s angle as 90°. All the external angles make straight angle with the internal angles. Therefore all the angles would be 90°. The information provided about the perimeter is of no use.
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4. Find the value of x.
mathematics-questions-answers-sum-measures-exterior-angles-polygon-q4
a) 160°
b) 140°
c) 120°
d) 150°
View Answer

Answer: a
Explanation: As we know that sum of all the internal angles of the triangle is 180°.
Therefore x+y+z=180°
Therefore 30°+130°+z=180°
Therefore z=120°
Now we know that the external angle is always a linear angle.
Therefore x+y=180°
Therefore 20°+y=180°
Therefore y=160°.

5. In the given figure find the values of x & y respectively.
mathematics-questions-answers-sum-measures-exterior-angles-polygon-q5
a) 14° & 166°
b) 166° & 14°
c) 170° & 10°
d) 10° & 170°
View Answer

Answer: b
Explanation: The polygon in the adjoining figure is a hexagon. In order to find the value of x we ought to know the sum of all the internal angles of any hexagon. The formula used is (n-2)180°. Therefore we get the sum of all the angles as 720°.
Therefore 84°+126°+149°+x°+104°+91°=720°
Therefore x=166°
Now we use the property of external angles and find the value of y.
Therefore x+y=180°
Therefore y=14°.
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6. In any equilateral triangle, find the sum of all the external angles.
a) 180°
b) 120°
c) 60°
d) 360°
View Answer

Answer: d
Explanation: As we know from our prior knowledge that all the angles in any equilateral triangle the angles measure 60°. Therefore the external angle would be measuring 120° as the pair of internal and external angles is always linear. Since there are three identical external angles, therefore our answer would be 120 ×3=360°.

7. Find the value of x.
mathematics-questions-answers-sum-measures-exterior-angles-polygon-q7
a) 3/140
b) 150/7
c) 140/3
d) 7/150
View Answer

Answer: c
Explanation: Here we are given a triangle with all it’s internal angles marked in terms of x.
Now we will use the property of triangle.
Therefore (x+20)°+(x+30)°+(x-10)°=180°
Therefore x+20+x+30+x-10=180
Therefore 3x=140
Therefore x=140/3.
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8. Find the value of x.
mathematics-questions-answers-sum-measures-exterior-angles-polygon-q8
a) 170/2°
b) 2/170°
c) 170°
d) 70°
View Answer

Answer: a
Explanation: Here we will use the property of external angles.
Therefore (x-10)°+x=180°
Therefore x-10+x=180°
Therefore 2x=170
Therefore x=170/2.

9. External angle and internal angle of a same polygon form a pair of linear angle together.
a) True
b) False
View Answer

Answer: a
Explanation: External angle of any polygon can be seen when the side of the polygon is extended and hence the external angle and the internal angle form a pair of linear angle. The sum of these two angles is always equal to 180°. They are also known as straight angles.
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10. A polygon can have each of its exterior angles as 70°.
a) True
b) False
View Answer

Answer: b
Explanation: Each exterior angle of any n-sided polygon=(360°)/n
If the exterior angle is 70°,
Then (360°)/n = 70
Therefore n=5.1. Here ‘n’ is the number of sides and since the number of sides cannot be any decimal number the answer to the statement is false.

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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