Question

In ΔUVW, m, angle, U, equals, left bracket, x, minus, 6, right bracket, degreesm∠U=(x−6) ∘ , m, angle, V, equals, left bracket, 5, x, plus, 6, right bracket, degreesm∠V=(5x+6) ∘ , and m, angle, W, equals, left bracket, 3, x, plus, 18, right bracket, degreesm∠W=(3x+18) ∘ . What is the value of x, question markx?

Answer 1

To find the value of x in triangle UVW, we sum the angles represented by the expressions (x - 6), (5x + 6), and (3x + 18) and set the sum equal to 180 degrees. Upon solving the equation, we find that x equals 18.

Step-by-step explanation:

The question involves finding the value of x in triangle UVW with given expressions for the measures of the angles. To solve for x, we use the fact that the sum of the interior angles in any triangle is 180 degrees. Setting up the equation using the expressions for angles U, V, and W, we have:

(x - 6) + (5x + 6) + (3x + 18) = 180

Combining like terms gives us:

9x + 18 = 180

Subtracting 18 from both sides:

9x = 162

Dividing both sides by 9:

x = 18

Therefore, the value of x is 18 degrees.