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4 December, 22:14

The angles in a triangle are such that one angle is 78 degrees more than the smallest angle, while the third angle is 4 times as large as the smallest angle. Find the measures of all three angles.

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  1. 4 December, 22:29
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    Let the angles are x, y and z.

    Let the smallest angle is x

    one angle is 78 degrees more than the smallest angle.⇒ y = x + 78 → (1)

    the third angle is 4 times as large as the smallest angle. ⇒ z = 4 x → (2)

    we should know that the sum of the angles of the triangle = 180°

    ∴ x + y + z = 180 → (3)

    substitute from (1) and (2) at (3)

    ∴ x + (x + 78) + (4x) = 180

    ∴ 6x = 180 - 78 = 102

    ∴ x = 102 : 6 = 17°

    ∴ y = 17 + 78 = 95°

    ∴ z = 4x = 68°

    So, the measures of all three angles are 17°, 95° and 68°
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