Sum of the Measures of the Exterior Angles Quiz - CBSE Class 8 Mathematics
Free practice quiz: Sum of the Measures of the Exterior Angles (CBSE Class 8 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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What is the sum of the measures of the exterior angles of a quadrilateral?
- 90 degrees
- 180 degrees
- 270 degrees
- 360 degrees
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Answer: D. 360 degrees
The sum of the measures of the exterior angles of any polygon, including a quadrilateral, is always 360 degrees.
Two exterior angles of a quadrilateral measure 75 degrees and 100 degrees respectively. If the other two exterior angles are equal, what is their measure?
- 92.5 degrees
- 87.5 degrees
- 185 degrees
- 90 degrees
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Answer: A. 92.5 degrees
Let x be the measure of each of the equal angles. Then 75 + 100 + 2x = 360. Solving for x: 2x = 185, x = 92.5 degrees.
Prove that the sum of the exterior angles of a convex polygon is 360 degrees using the concept of the sum of interior angles.
- Proof by induction is needed
- This cannot be proven using interior angles
- Consider the sum of interior and exterior angles at each vertex
- The sum is not always 360 degrees
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Answer: C. Consider the sum of interior and exterior angles at each vertex
At each vertex, the sum of the interior and exterior angles is 180 degrees. The sum of all interior angles is (n-2)180 degrees where n is the number of sides. Subtracting this from the sum of interior and exterior angles proves the theorem.
A regular octagon has exterior angles of equal measure. What is the measure of each exterior angle?
- 45 degrees
- 90 degrees
- 135 degrees
- 36 degrees
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Answer: A. 45 degrees
360/8 = 45
If the ratio of the exterior angles of a quadrilateral is 1:2:3:4, what is the measure of the smallest exterior angle?
- 36 degrees
- 72 degrees
- 108 degrees
- 144 degrees
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Answer: A. 36 degrees
10x = 360; x = 36