In triangle $ABC$, the angles $\angle A$, $\angle B$, $\angle C$ form an arithmetic sequence. If $\angle A = 23^\circ$, then what is $\angle

Question

In triangle $ABC$, the angles $\angle A$, $\angle B$, $\angle C$ form an arithmetic sequence. If $\angle A = 23^\circ$, then what is $\angle C$, in degrees? if u can’t understand latex then: In triangle ABC, the angles,angle A, angle B, angle C form an arithmetic sequence. If angle A = 23 degrees, then what is angle C, in degrees?

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Mia 3 weeks 2022-01-07T14:58:19+00:00 1 Answer 0 views 0

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    2022-01-07T14:59:36+00:00

    Answer:

    97^0

    Step-by-step explanation:

    Given that the angles A, B, C in a Triangle form an arithmetic sequence where A=23 degrees.

    The nth term of an Arithmetic sequence is given by the formula: T_n=a+(n-1)d

    Where:

    a=first term

    n=number of term

    d=common difference

    In this case,

    Angle \:A, a=23^0

    Angle B, T_2=23+(2-1)d=(23+d)^0\\Angle C, T_3=23+(3-1)d=(23+2d)^0

    The sum of angles in a triangle is 180 degrees. Therefore:

    ∠A+∠B+∠C=180 degrees

    23^0+(23+d)^0+(23+2d)^0=180\\69^0+3d=180^0\\3d=180^0-69^0\\3d=111^0\\d=37^0

    Therefore:

    Angle C,

    (23+2d)^0=(23+2(37))^0=23+74\\C=97^0

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