Given a right triangle where $\angle VUW$ = $4x+6$ degrees and $\angle WUT$ = $6x-10$ degrees, what is the value of $x$?

• A. $13$
• B. $10$
• C. $8$
• D. $16$

Answer: (A)

Verified step by step guidance

1. Identify that the problem involves a right triangle, which means the sum of the three interior angles is 180 degrees, and one of the angles is 90 degrees.
2. Recognize that the two given angles, \( \angle VUW = 4x + 6 \) degrees and \( \angle WUT = 6x - 10 \) degrees, are the two non-right angles in the triangle.
3. Set up the equation using the fact that the sum of the two non-right angles must be 90 degrees because the right angle accounts for the other 90 degrees: \[(4x + 6) + (6x - 10) = 90\]
4. Simplify the equation by combining like terms: \[4x + 6x + 6 - 10 = 90\] \[10x - 4 = 90\]
5. Solve for \( x \) by isolating it on one side: \[10x = 90 + 4\] \[10x = 94\] \[x = \frac{94}{10}\]