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in Lines and Angles by (44.3k points)

Find the angle whose complement is one third of its supplement.

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Best answer

Consider the required angle as x°

We know that the complement can be written as 90° – x° and the supplement can be written as 180° – x°

90° – x° = 1/3(180° – x°)

We can also write it as

90° – x° = 60° – (1/3) x°

So we get

x° – (1/3)x° = 90° – 60°

(2/3) x° = 30°

By division we get

x° = ((30×3)/2)

x° = 45°

Therefore, the angle whose complement is one third of its supplement is 45°.

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