In ΔVWX, {VX} is extended through point X to point Y, m∠VWX = (3x+2)) ∘ , m∠WXY = (6x-19)∘ , and m∠XVW = (x+17)^{\circ}(x+17) ∘ . Find m∠XVW

Question

In ΔVWX, {VX} is extended through point X to point Y, m∠VWX = (3x+2)) ∘ , m∠WXY = (6x-19)∘ , and m∠XVW = (x+17)^{\circ}(x+17) ∘ . Find m∠XVW.In ΔVWX, \overline{VX} VX is extended through point X to point Y, m∠VWX = (3x+2)^{\circ}(3x+2) ∘ , m∠WXY = (6x-19)^{\circ}(6x−19) ∘ , and m∠XVW = (x+17)^{\circ}(x+17) ∘ . Find m∠XVW.

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Sophia 1 week 2021-10-11T20:05:41+00:00 1 Answer 0

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    2021-10-11T20:06:44+00:00

    Answer:

    ∠XVW = 36°

    Step-by-step explanation:

    The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

    ∠WXY is an external angle to the triangle and

    ∠XVW and ∠VWX are the 2 opposite interior angles, thus

    6x – 19 = x + 17 + 3x + 2, that is

    6x – 19 = 4x + 19 ( subtract 4x from both sides )

    2x – 19 = 19 ( add 19 to both sides )

    2x = 38 ( divide both sides by 2 )

    x = 19

    Hence

    ∠XVW = x + 17 = 19 + 17 = 36°

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