If the three angles of a triangle are (x+15°), (6x/5+6°) and (2x/3+30°), prove that the triangle is an equilateral triangle​

Question

If the three angles of a triangle are (x+15°), (6x/5+6°) and (2x/3+30°), prove that the triangle is an equilateral triangle​

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Eloise 4 days 2021-10-11T12:24:03+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-11T12:25:18+00:00

    Step-by-step explanation:

    Three angles are (x+15)°, (6x/5+6)°, (2x/3+30)°

    By condition

    (x+15)°+(6x/5+6)°+(2x/3+30)° = 180°

    (x+15)+(6x/5+6)+(2x/3+30) = 180

    x+15+6x/5+6+2x/3+30 = 180

    x+15+6x/11+2x/33 = 180

    x+6x/11+2x/33+15 = 180

    33x+18x+2x/33 = 180

    53x/33 = 180

    x = 180×33/53

    Please do the next by yourself

    0
    2021-10-11T12:25:56+00:00

    Step-by-step explanation:

    method 1

    in equilateral triangle all angles are 60°

    angle 1

    angle \: 1 \\ x + 15 = 60 \\ x = 60 - 15 \\ x = 45 \\  \\ angle \: 2 \\  \frac{6x}{5} + 6 = 60 \\  \frac{6x}{5}   = 60 - 6 \\  \frac{6x}{5}  = 54 \\ 6x = 54 \times 5 \\ x =  \frac{54 \times 5}{6}  \\ x = 9 \times 5 \\ x = 45 \\  \\ angle \: 3 \\  \frac{2x}{3}  + 30 = 60 \\  \frac{2x}{3}  = 60 - 30 \\  \frac{2x}{3}  = 30 \\ 2x = 30 \times 3 \\ 2x = 90 \\ x =  \frac{90}{2}  \\ x = 45

    all the x value are 45°

    method 2

    sum of all angles of a triangle is 180°

    x + 15 +  \frac{6x}{5}  + 6 +  \frac{2x}{3}  + 30 = 180 \\ x +  \frac{6x}{5}  +  \frac{2x}{3}  + 51 = 180 \\  \\ x +  \frac{6x}{5}  +  \frac{2x}{3}  = 180 - 51 \\  \frac{15x + 18x + 10x}{15}  = 129 \\  \frac{43x}{15}  = 129 \\ 43x = 129 \times 15 \\ x =  \frac{129 \times 15}{43}  \\ x = 3 \times 15 \\ x = 45

    all the angels are equal to 60° hence it forms an equilateral triangle

    hope you get your answer

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