1. What is the sum of the interior angles of any quadrilateral?
- A180 deg
- B270 deg
- C360 deg
- D540 deg
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Answer: C) 360 deg
A quadrilateral can be split into 2 triangles by one diagonal, so angle sum = 2 x 180 = 360 deg.
Class 8 Angle Sum of Polygons — practice questions with answers
Quadrilaterals · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. An interior angle and its adjacent exterior angle in a polygon add up to:
- A90 deg
- B180 deg
- C270 deg
- D360 deg
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Answer: B) 180 deg
An interior angle and its exterior angle form a straight line (linear pair), so they sum to 180 deg.
3. In quadrilateral PQRS, angle P = 90 deg, angle Q = 90 deg, angle R = 90 deg. Find angle S.
- A180
- B81
- C99
- D90
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Answer: D) 90
angle S = 360 - (90 + 90 + 90) = 360 - 270 = 90 deg.
4. A regular polygon has 15 sides (a regular pentadecagon used on a coin design).
What is the measure of each exterior angle?
What is the measure of each exterior angle?
- A20 deg
- B24 deg
- C30 deg
- D36 deg
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Answer: B) 24 deg
Each exterior angle = = 24 deg.
5. In quadrilateral KLMN, angle K = (2x) deg, angle L = (x + 25) deg, angle M = (2x - 30) deg and angle N = (x + 5) deg.
Find the measure of angle L.
Find the measure of angle L.
- A75 deg
- B85 deg
- C95 deg
- D105 deg
Show answer
Answer: B) 85 deg
Sum: 2x + (x+25) + (2x-30) + (x+5) = 360, so 6x + 0 = 360, x = 60. angle L = x + 25 = 60 + 25 = 85 deg. (Check: 120 + 85 + 90 + 65 = 360.)
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