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) ∘

Question

3 years ago

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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.

Mathematics

1 answer:

blagie [28] · Answer 1 · 2022-08-22T12:35:04+03:00

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°