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Question
The measure of an angle which is four times its supplement is ______.
Options
36°
144°
16°
64°
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Solution
The measure of an angle which is four times its supplement is 144°.
Explanation:
Let the required angle be x.
Then, its supplement will be (180° – x).
It is given that, the angle is four times its supplement.
Therefore, x = 4(180° – x)
⇒ x = 4 × 180° – 4x
⇒ x + 4x = 720°
⇒ 5x = 720°
⇒ x = `720^circ/5`
⇒ x = 144°
Hence, the required angle is 144°.
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