Final answer:
The value of x is found by setting up an equation based on the fact that the angles around point v add up to 360°. After simplifying the equation, the value of x is determined to be approximately 24.
Step-by-step explanation:
The question involves finding the value of x given the angle measurements in a geometric figure. The angle measurements are m∠tuv=(2x + 20)°, m∠uvw=(8x + 12)°, and m∠vtu=(3x + 19)°. To solve for x, we can use the fact that the sum of the angles around point v must equal 360° because they form a complete circle. This gives us the equation:
(2x + 20)° + (3x + 19)° + (8x + 12)° = 360°
Combining like terms, we get:
13x + 51 = 360
Subtracting 51 from both sides gives:
13x = 309
Dividing both sides by 13 gives:
x = 23.7692, which we can round to x = 24 for practical purposes.