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14 April, 03:01

An angle measures 30° less than the measure of its supplementary angle. What is the measure of each angle?

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  1. 14 April, 04:27
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    The measures of each would be:

    105° and 75°

    Step-by-step explanation:

    Supplementary angles are two angles whose measures sum up to 180° or they form a straight line.

    So if an angle measures 30° less than the measure of its supplementary, it wold mean that both angles together is equal to 180°.

    ∠1 = x

    ∠2 = x-30°

    ∠1 + ∠2 = 180°

    So here we plug in our equations:

    ∠1 + ∠2 = 180°

    x + x - 30° = 180°

    2x - 30° = 180°

    We solve for the x then:

    Add 30° on both sides of the equation:

    2x - 30° + 30° = 180° + 30°

    2x = 210°

    Divide both sides by 2:

    2x/2 = 210°/2

    x = 105°

    ∠1 = 105°

    Now we solve for the second angle:

    ∠1 + ∠2 = 180°

    105° + ∠2 = 180°

    Subtract 105° from both sides of the equation:

    105° + ∠2 - 105° = 180° - 105°

    ∠2 = 75°
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