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The measure of one of the equal angles in an isosceles triangle is twice the measure of the remaining angle. Determine the exact radian measures of the three angles in the triangle.

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  1. Let each of the equal angles be A.
    Since we know that the angles of a triangle add up to 180°, we determine that the third angle is (180-2A)°.
    Thus
    A=2(180-2A)
    5A = 360
    A = 72
    Therefore the angles are 72°, 72° and 36°.

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  2. Let x represent the 3rd angle
    Thus 2x represents the other 2 angles
    We know that a triangle totals 180 degress
    180 = x + 2(2x)
    180 = 5x
    x = 36 degrees
    2x
    2(36) = 72 degrees
    Convert to radians using the pi/180 formula
    Therefore the angles are pi/5, 2pi/5, 2pi/5

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