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°.