Final answer:
To solve for x when given the measures of angles DFG and EFG in degrees, set up an equation assuming the angles form a linear pair, solve for x, and find that x equals 37 degrees.
Step-by-step explanation:
To find the value of x when m∠dfg=(2x+6)° and m∠efg=(3x-11)°, we assume that angles DFG and EFG form a linear pair which means they add up to 180°. The equation would therefore be:
- (2x + 6)° + (3x - 11)° = 180°
Simplifying this equation:
- Combine like terms: 2x + 3x + 6 - 11 = 180
- 5x - 5 = 180
- Add 5 to both sides: 5x = 185
- Divide by 5: x = 37
Thus, the value of x is 37°.