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29 July, 04:55

Two angles are supplementary. The measure of the larger angle is 12 degrees more than three times the smaller angle. Find the measures of the angles

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  1. 29 July, 06:22
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    Measure of first angle: 42 degrees,

    Measure of second angle: 138 degrees

    Step-by-step explanation:

    Let us say x ⇒ measure of the smaller angle, y ⇒ measure of the larger angle

    1. Now given that the measure of the larger angle is 12° more than 3 times the smaller angle: y = 12 + 3x

    2. If these angles are supplementary, we could formulate another equation were the two angles add to 180°: x + y = 180

    3. In this situation it is convenient to apply substitution as to solve for x, y:

    1. x + (12 + 3x) = 180

    2. x + 12 + 3x = 180

    3. 4x + 12 + 180

    4. 4x = 168

    5. x = 42 degrees

    4. Now substitute this value of x into the first equation y = 12 + 3x, and to solve for y as well:

    1. y = 12 + 3 (42)

    2. y = 12 + 126

    3. y = 138 degrees
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