Final answer:
To find the value of X when DE bisects angle ABC, set up an equation with the given values and solve for X. However, the solution to the equation does not match any of the provided options, implying there may be a misunderstanding of the question or an error in the options.
Step-by-step explanation:
When line DE bisects angle ABC, it means it divides angle ABC into two equal smaller angles. Given that angle ABC is equal to 7X plus 29, and angle DBG equals 99°, we can set up an equation since the bisected angles are equal to each other:
7X + 29 = 2 * angle DBG
Since angle DBG equals 99°, we can substitute:
7X + 29 = 2 * 99°
7X + 29 = 198°
Now we solve for X:
7X = 198° - 29°
7X = 169°
X = 169° / 7
X = 24.14, which is not an option provided, but since the question might be misinterpreted without the exact diagram, if we assume that angle ABC is split into angle DBG and another angle which equals 7X + 29, then:
7X + 29 + 99° = 180° (since the angles in a triangle add up to 180°)
7X + 128° = 180°
7X = 180° - 128°
7X = 52°
X = 52° / 7
X = 7.43, which is also not a provided option. Therefore, there could be an error in the provided options or the initial question.