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
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°.
2. The sum total of all the external angles is always ________
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?
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.
Explanation: As we know that sum of all the internal angles of the triangle is 180°.
Now we know that the external angle is always a linear angle.
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°.
Now we use the property of external angles and find the value of y.
6. In any equilateral triangle, find the sum of all the external angles.
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°.
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.
Explanation: Here we will use the property of external angles.
9. External angle and internal angle of a same polygon form a pair of linear angle together.
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.
10. A polygon can have each of its exterior angles as 70°.
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.
To practice Mathematics Exam Questions and Answers for Class 8, here is complete set of 1000+ Multiple Choice Questions and Answers.