Question

In AWXY, WY is extended through point Y to point Z, YWX = (3x + 17), XYZ = (10x – 5), and WXY = (3x - 2). Find WXY.

Answer 1

Let's draw the figure to better understand the scenario:

To be able to get the measure of ∠WXY, we will be using the relationship of the interior angles of a triangle.

The sum of all interior angles of a triangle is 180°. Therefore we can say,

$\text{ }\angle YWX\text{ + }\angle WXY\text{ + }\angle XYW=180^{\circ}$

The formula or measure of ∠XYW isn't given. However, we observed that ∠XYW and ∠XYZ are pairs of Supplementary Angles. This means that the sum of two angles is equal to 180°.

We get,

$\text{ }\angle XYW\text{ + }\angle XYZ=180^{\circ}$

Therefore,

$\text{ }\angle XYW\text{ }=180^{\circ}\text{ - }\angle XYZ$

We will use this to complete the formula of the sum interior angles, substituting ∠XYW = 180° - ∠XYZ.

$\text{ }\angle YWX\text{ + }\angle WXY\text{ + }\angle XYW=180^{\circ}$$\text{ }\angle YWX\text{ + }\angle WXY\text{ + (}180^{\circ}-\angle XYZ)=180^{\circ}$

Substituting the given formulas of each angle, let's find x.

$\text{ }\angle YWX\text{ + }\angle WXY\text{ + (}180-\angle XYZ)=180^{\circ}$$(3x+17)+(3x-2)+(180-(10x-5)^{})=180^{\circ}$$\text{-4x + 200 = 180}$$\text{-4x = 180 - 200 = -20}$$\frac{\text{-4x}}{-4}\text{ = }\frac{\text{-20}}{-4}$$\text{ x = 5}$

Let's substitute x = 5 to ∠WXY = 3x - 2 to find its measure.

$\angle WXY=3x-2=\text{ 3(5) - 2}$$\text{ = 15 - 2}$$\angle WXY=13^{\circ}$

Therefore, the measure of ∠WXY = 13°.