Class 9 Angle Sum Property of Quadrilaterals — practice questions with answers
Geometry — Quadrilaterals · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. What is the sum of all four 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 by one diagonal into 2 triangles. Each triangle has angle sum 180 deg, so 2 x 180 = 360 deg.
2. The angles of a quadrilateral are 2x, 3x, 4x and 6x. Find the value of x.
A24
B26
C48
D22
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Answer: A) 24
2x + 3x + 4x + 6x = 15x = 360, so x = 24.
3. The angles of a quadrilateral are x, 2x, 2x and 3x. The largest angle is:
A90 deg
B120 deg
C135 deg
D150 deg
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Answer: C) 135 deg
x + 2x + 2x + 3x = 8x = 360, so x = 45. Largest = 3x = 135 deg.
4. Consider a quadrilateral in which one interior angle is reflex (a concave quadrilateral). Three of the ordinary interior angles measure 50 deg, 40 deg and 70 deg. Using the angle sum of 360 deg, find the measure of the fourth (reflex) interior angle.
A400
B200
C220
D180
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Answer: B) 200
Fourth angle = 360 - (50 + 40 + 70) = 360 - 160 = 200 deg, which is reflex (greater than 180).
5. In quadrilateral ABCD, angle A = (x + 30), angle B = (2x), angle C = (x + 40) and angle D = (2x - 10) degrees. Find x, then check whether opposite angles A and C are supplementary (sum to 180). What is the sum of angle A and angle C?
A170
B340
C155
D185
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Answer: A) 170
Sum: (x+30)+(2x)+(x+40)+(2x-10) = 6x + 60 = 360, so 6x = 300, x = 50. angle A = 80, angle C = 90, A + C = 170 deg, which is NOT 180, so A and C are not supplementary.