one side of triangle is produced and the exterior opposite angle be in ratio 3:5 find the measures of each angle of triangle. please an

Question

one side of triangle is produced and the exterior opposite angle be in ratio 3:5 find the measures of each angle of triangle.
please answer me first

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Savannah 4 days 2021-10-11T08:35:37+00:00 1 Answer 0 views 0

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    2021-10-11T08:36:40+00:00

    Answer:

    have the property that, in a triangle exterior angle is equal to the sum of interior opposite angles.

    Given, the interior opposite angles to the exterior angle 105

    are in the ration 2:5

    ∴2x+5x=105

    o

    7x=105

    o

    ⟹x=15

    o

    Therefore the interior opposite angles to the angle 105

    o

    are 2x=2(15)=30

    o

    and 5x=5(15)=75

    o

    Let the third angle of the triangle be C

    We have the sum of interior angles of a triangle is 180

    o

    ∴30

    o

    +75

    o

    +C=180

    o

    C=180

    o

    −75

    o

    −30

    o

    =180

    o

    −105

    o

    C=75

    o

    Hence, the angles are 30

    o

    ,75

    o

    ,75

    o

    .

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