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.

The measure of the angle XVW is:

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

Recall:

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

In triangle VWX,

Therefore:

(exterior angle theorem)

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∠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°

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24