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.

Answer 1

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°

Answer 2

The measure of the angle XVW is:

$\mathbf{m\angle XVW =36^{\circ}}$

The exterior angle theorem would be applied to create an equation that will help us in finding the value of x, first.

Recall:

• Exterior angle theorem states that the sum of two interior angles in a triangle will be equal to the exterior angle of the triangle that is opposite the two interior angles.

(The figure showing triangle VWX is provided in the attachment below)

In triangle VWX,

• <VWX and <XVW are interior angles

• <WXY is the exterior angle.

Therefore:

$(3x +2) + (x + 17) = (6x - 19)$ (exterior angle theorem)

• Solve for x

$3x +2 + x + 17 = 6x - 19$

• Add like terms

$4x + 19 = 6x - 19\\\\4x - 6x = -19-19\\\\-2x = -38$

• Divide both sides by -2

$x = 19$

• Let's find m∠XVW:

$m\angle XVW = x + 17$

• Plug in the value of x

$m\angle XVW = 19 + 17\\\\m\angle XVW =36^{\circ}$

• Therefore, $\mathbf{m\angle XVW =36^{\circ}}$

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