Final answer:
By using the sum of angles in a triangle, we determined that the value of x is 12, resulting in the angles of the triangle being 35°, 90°, and 55°.
Step-by-step explanation:
To find the value of x and the measure of each angle in a triangle, you can use the fact that the sum of the angles in a triangle adds up to 180 degrees. Given the angles in the question are (2x + 11)°, (5x + 30)°, and (4x + 7)°, we can set up the equation:
(2x + 11) + (5x + 30) + (4x + 7) = 180
Combining like terms, we get:
11x + 48 = 180
Subtracting 48 from both sides, we get:
11x = 132
Dividing both sides by 11, we find:
x = 12
Now we can find each angle:
- First angle: (2x + 11)° = (2×12 + 11)° = 35°
- Second angle: (5x + 30)° = (5×12 + 30)° = 90°
- Third angle: (4x + 7)° = (4×12 + 7)° = 55°
Hence, the value of x is 12, and the angle measures are 35°, 90°, and 55° respectively.