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13 December, 09:50

In a triangle, the measure of the second angle is twice the measure of the first angle. the third angel is equal to the sum of the other angels

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  1. 13 December, 10:07
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    So the angles have measurements 30,60, and 90 degrees.

    Step-by-step explanation:

    We have a triangle which means the interior angles of that triangle has sum 180 degrees.

    Let's call the angle measurements: A, B, and C.

    A+B+C=180

    B=2A (The second angle is twice the first.)

    C=A+B (The third angle is the sum of the other 2.)

    If C=A+B, then C=A+2A (since B=2A).

    So we have this system:

    A+B+C=180

    B=2A

    C=3A (since C=A+2A=3a).

    Now I'm going to use the first equation A+B+C=180 and plug in the other equations we have below it:

    A+B+C=180 with B=2A and C=3A.

    A+2A+3A=180

    6A=180

    Divide both sides by 6:

    A=180/6

    A=30

    If B=2A and A=30, then B=2 (30) = 60.

    If C=3A and A=30, then C=3 (30) = 90.

    So the angles have measurements 30,60, and 90 degrees.
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