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In an isoceles triangle top vertex is twice the of the sum of the base angle.find all the exterior angles of the triangle?

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  1. If it is an isosceles triangle the two base angles will be equal.

    Let the base angle be a, then the vertex angle will be:

    180° - 2 a

    According to the condition:

    Top vertex is twice the of the sum of the base angle:

    180° - 2 a = 2 ( a + a )

    180° - 2 a = 2 * 2a

    180° - 2 a = 4 a Add 2 a to both sides

    180° - 2 a + 2 a = 4 a + 2 a

    180° = 6 a Divide both sides by 6

    180° / 6 = a

    30° = a

    a = 30 °

    So the base angles are 30° and the vertex angle is 180° - 2 * 30° = 180° - 60° = 120 °

    Exterior base angle is 360° - 30° = 330°

    The exterior vertex angle is 360° - 120° = 240°

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  2. I believe exterior angles are 180 - interior angles. Their sum is 360.

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