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Question
The angles of a quadrilateral are in A.P. whose common difference is 10°. Find the angles.
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Solution
Let the angles be \[(A)^\circ, (A + d)^\circ, (A + 2d)^\circ, (A + 3d)^\circ, \]
Here, d = 10
So,
\[\left( A \right)^\circ, (A + 10)^\circ, (A + 20)^\circ, (A + 30)^\circ,\] are the angles of a quadrilateral whose sum is 360o.
are the angles of a quadrilateral whose sum is 360o.
\[\therefore \left( A \right)^\circ, (A + 10)^\circ, (A + 20)^\circ,(A + 30)^\circ, = 360^\circ,\]
\[ \Rightarrow 4A = 360 - 60\]
\[ \Rightarrow A = \frac{300}{4} = 75^\circ,\]
\[\text { The angles are as follows: } \]
\[75^\circ,(75 + 10)^\circ, (75 + 20)^\circ,(75 + 30)^\circ, i . e . 75^\circ, 85^\circ, 95^\circ,105^\circ,\]
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