Question

1. find the measure of ∠dog. 27x + 4 16x + 4

Explanation:

Step1: Set up equation for vertical - angles

Vertical angles are equal. So, $27x + 4=16x + 4$.
Subtract $16x$ from both sides: $27x-16x + 4=16x-16x + 4$, which simplifies to $11x+4 = 4$.
Subtract 4 from both sides: $11x+4 - 4=4 - 4$, getting $11x=0$, so $x = 0$.

Step2: Find the measure of an angle related to $\angle DOG$

Let's assume $\angle DOG$ is related to the angles at point E. If we consider the linear - pair or vertical - angle relationships, we need more information about the connection between the angles at E and $\angle DOG$. But if we assume that the angle adjacent to $27x + 4$ and $\angle DOG$ are vertical angles.
The angle with measure $27x + 4$ (when $x = 0$) has measure $27\times0+4=4$.
If $\angle DOG$ is a vertical angle to an angle of measure $4$, then $\angle DOG = 4$.

Answer:

$4$