Question

question 6 (2 points) find m∠4. complete the reasoning: m∠4 = 62 ° because it is a angle with the given. x = 7 (8x + 6)° 118° 4 blank 1: 62 blank 2: t blank 3: 7 question 7 (2 points) find m∠5. complete the reasoning: m∠5 = 65 ° is a corresponding angle with the given.

Explanation:

Step1: Use linear - pair property

The angle adjacent to the $118^{\circ}$ angle forms a linear - pair. A linear - pair of angles sums to $180^{\circ}$. Let the adjacent angle be $A$. Then $A + 118^{\circ}=180^{\circ}$, so $A = 180^{\circ}-118^{\circ}=62^{\circ}$.

Step2: Identify angle relationship

$\angle4$ and the angle $A$ are vertical angles. Vertical angles are equal. So $m\angle4 = 62^{\circ}$.

Step3: Solve for $x$

The angle $(8x + 6)^{\circ}$ and the $118^{\circ}$ angle are corresponding angles (assuming the lines are parallel as indicated by the arrow marks). Corresponding angles are equal. So we set up the equation $8x+6 = 118$.
Subtract 6 from both sides: $8x=118 - 6=112$.
Divide both sides by 8: $x=\frac{112}{8}=14$. But it seems there is an error in the problem - setup as the given $x = 7$ does not satisfy the angle - equality relationship for the parallel lines. If we assume the problem is about vertical/linear - pair relationships only for $\angle4$ and ignore the $x$ part related to the parallel - line assumption for now, the reason for $m\angle4 = 62^{\circ}$ is that it is a vertical angle with the angle adjacent to the $118^{\circ}$ angle.

Answer:

Blank 1: 62
Blank 2: vertical
Blank 3: 7 (although the value of $x$ calculated from the parallel - line angle relationship is 14)