Question
The angles of a quadrilateral are in AP whose common difference is 10º. Find the angles.Hint: Let these angles be xº, (x + 10)º, (x + 20)º and (x + 30)º.
Their sum is 360º.
Their sum is 360º.
✓
Answer
Let the required angles be (a - 15)º, (a - 5)º, (a + 5)º, and (a + 15)º as the common difference is 10 (given).
Then (a - 15)º + (a - 5)º + (a + 5)º + (a + 15)º = 360º
⇒ 4a = 360
⇒ a = 90
Hence, the required angles of a quadrilateral are
(90 - 15)º, (90 - 5)º, (90 + 5)º and (90 + 15)º; or 75º, 85º, 95º and 105º.
Then (a - 15)º + (a - 5)º + (a + 5)º + (a + 15)º = 360º
⇒ 4a = 360
⇒ a = 90
Hence, the required angles of a quadrilateral are
(90 - 15)º, (90 - 5)º, (90 + 5)º and (90 + 15)º; or 75º, 85º, 95º and 105º.
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