Q1 of 40 Page 8

In a quadrilateral ABCD, the angles A, B, C, and D are in ratio 1: 2: 4: 5. Find the measure of each angle of the quadrilateral.

Given: The angles of a quadrilateral are in ratio 1: 2: 4: 5

To Find: Measure each angle.


Concept Used:


Sum of angles of a quadrilateral = 360˚


Assumption: Let the angles of quadrilateral be


∠A = x˚


∠B = 2x˚


∠C = 4x˚


∠D = 5x˚


Explanation:


X + 2x + 4x + 5x = 360˚


12x = 360˚



X = 30˚


Therefore,


X = 30˚


2x = 2 × 30˚ = 60˚


4x = 4 × 30˚ = 120˚


5x = 5 × 30˚ = 150˚


Hence, the angles of a quadrilateral are 30˚, 60˚, 120˚, and 150˚.


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(ii) AG = 2AF 2

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