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Question

Two angles of a quadrilateral measure 80o each. The other two differ by 20o. What is the measure of each of the other angles.

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Solution

Let x and y be the other two angles such that x>y.
Now,
xy=20°.....(1)
Also,
80°+80°+x+y=360°(Sum of interior angles of a quadrilateral)
x+y=360°160°=200°.....(2)
Adding equation (1) and (2), we get
2x=220°
x=220°2=110°
Substituting the value of x in equation (1), we have
y=x20°=110°20°=90°
Hence the other angles are 90° and 110° respectively.

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