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Question
The sum of two angles is 5πc and their difference is 60°. Find their measures in degrees.
Solution
We know that, 1c = `(180/pi)^circ`
∴ 5πc = `(5pi xx 180/pi)^"c"` = 900°
Let the degree measures of the angles be x and y.
Then x + y = 900° ...(1)
and x – y = 60° ...(2)
2x = 960°
x = 480°
Adding (1) and (2), we get,
2x = 960° ∴ x = 480°
∴ Substituting the value of x in (1), we get
480° + y = 900°
∴ y = 900° − 480°
∴ y = 420°
Hence, the degree measures of the two angles are 480° and 420°.
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