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Which polygon has both its interior and exterior angles the same?
- a)Triangle
- b)Quadrilateral
- c)Pentagon
- d)Hexagon
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Which polygon has both its interior and exterior angles the same?a)Tri...
We know that
Interior angle + Exterior angle = 180 degrees
If Interior angle = Exterior angle
Then Exterior angle + Exterior angle = 180 degrees
2 Exterior angle = 180 degrees
Exterior angle = 180 / 2
Exterior angle = 90.
But Interior angle = Exterior angle = 90 deg
Number of sides n = 360/(180 – interior angle)
n = 360 /( 180 – 90)
n = 360 / 90
n = 4.
A polygon with 4 sides has both interior angles and exterior angles as same.
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Community Answer
Which polygon has both its interior and exterior angles the same?a)Tri...
Quadrilateral
A polygon is a closed figure with straight sides. The interior angles of a polygon are the angles formed inside the shape, while the exterior angles are the angles formed outside the shape.
Interior angles of a quadrilateral:
- A quadrilateral has four sides, so it also has four interior angles.
- To find the sum of the interior angles of a quadrilateral, we use the formula (n-2) * 180 degrees, where n represents the number of sides.
- For a quadrilateral, the sum of the interior angles is (4-2) * 180 = 360 degrees.
- Therefore, the average measure of each interior angle in a quadrilateral is 360/4 = 90 degrees.
Exterior angles of a quadrilateral:
- An exterior angle of a polygon is formed by extending one of its sides.
- The sum of the exterior angles of any polygon is always 360 degrees.
- Therefore, in a quadrilateral, the sum of the exterior angles is 360 degrees.
- Since a quadrilateral has four exterior angles, each exterior angle measures 360/4 = 90 degrees.
Explanation:
- In a quadrilateral, both the interior angles and the exterior angles have the same measure of 90 degrees.
- This means that the interior angles and the exterior angles of a quadrilateral are congruent or equal in measure.
- Therefore, the correct answer to the question is option 'B' - Quadrilateral.
Summary:
- A quadrilateral is a polygon with four sides.
- The sum of the interior angles of a quadrilateral is 360 degrees, and each interior angle measures 90 degrees.
- The sum of the exterior angles of a quadrilateral is also 360 degrees, and each exterior angle measures 90 degrees.
- Hence, a quadrilateral has both its interior and exterior angles equal in measure.
A polygon is a closed figure with straight sides. The interior angles of a polygon are the angles formed inside the shape, while the exterior angles are the angles formed outside the shape.
Interior angles of a quadrilateral:
- A quadrilateral has four sides, so it also has four interior angles.
- To find the sum of the interior angles of a quadrilateral, we use the formula (n-2) * 180 degrees, where n represents the number of sides.
- For a quadrilateral, the sum of the interior angles is (4-2) * 180 = 360 degrees.
- Therefore, the average measure of each interior angle in a quadrilateral is 360/4 = 90 degrees.
Exterior angles of a quadrilateral:
- An exterior angle of a polygon is formed by extending one of its sides.
- The sum of the exterior angles of any polygon is always 360 degrees.
- Therefore, in a quadrilateral, the sum of the exterior angles is 360 degrees.
- Since a quadrilateral has four exterior angles, each exterior angle measures 360/4 = 90 degrees.
Explanation:
- In a quadrilateral, both the interior angles and the exterior angles have the same measure of 90 degrees.
- This means that the interior angles and the exterior angles of a quadrilateral are congruent or equal in measure.
- Therefore, the correct answer to the question is option 'B' - Quadrilateral.
Summary:
- A quadrilateral is a polygon with four sides.
- The sum of the interior angles of a quadrilateral is 360 degrees, and each interior angle measures 90 degrees.
- The sum of the exterior angles of a quadrilateral is also 360 degrees, and each exterior angle measures 90 degrees.
- Hence, a quadrilateral has both its interior and exterior angles equal in measure.
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Which polygon has both its interior and exterior angles the same?a)Triangleb)Quadrilateralc)Pentagond)HexagonCorrect answer is option 'B'. Can you explain this answer?
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Which polygon has both its interior and exterior angles the same?a)Triangleb)Quadrilateralc)Pentagond)HexagonCorrect answer is option 'B'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Which polygon has both its interior and exterior angles the same?a)Triangleb)Quadrilateralc)Pentagond)HexagonCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which polygon has both its interior and exterior angles the same?a)Triangleb)Quadrilateralc)Pentagond)HexagonCorrect answer is option 'B'. Can you explain this answer?.
Which polygon has both its interior and exterior angles the same?a)Triangleb)Quadrilateralc)Pentagond)HexagonCorrect answer is option 'B'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Which polygon has both its interior and exterior angles the same?a)Triangleb)Quadrilateralc)Pentagond)HexagonCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which polygon has both its interior and exterior angles the same?a)Triangleb)Quadrilateralc)Pentagond)HexagonCorrect answer is option 'B'. Can you explain this answer?.
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