Question

In ΔUVW, \overline{UW}

UW
is extended through point W to point X, angle WUV = (3x-4) and
angle VWX = (6x+6) and angle UVW = (x+20) What is the value of x?

Answer 1

Using the exterior angle theorem, we determine the value of x by setting up an equation with the given angle expressions. Upon simplifying and solving the equation, we find that x equals 5.

Step-by-step explanation:

To find the value of x in the extended triangle scenario, where lines and angles are given as expressions of x, we will use the exterior angle theorem. This theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

In ΔUVW, angle VWX is the exterior angle to angle UVW and angle WUV. Therefore, we have:

• angle WUV = (3x - 4)
• angle VWX = (6x + 6)
• angle UVW = (x + 20)

Applying the exterior angle theorem:

(3x - 4) + (x + 20) = (6x + 6)

Combining like terms we get:

4x + 16 = 6x + 6

Now, we'll solve for x:

16 - 6 = 6x - 4x

10 = 2x

Therefore, x = 5.