Question

the measure of angle 1 is 40
the measure of angle 2 is 124
the measure of angle 4 is 124
the measure of angle 7 is type your answer...

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle2$ and $\angle4$ are vertical angles, and $\angle2 = 124^{\circ}$, so $\angle4=124^{\circ}$. $\angle1$ and $\angle3$ are vertical angles, so $\angle3 = 40^{\circ}$.

Step2: Use linear - pair property

$\angle2$ and $\angle1+\angle5$ form a linear - pair. A linear - pair of angles sums to $180^{\circ}$. So $\angle1+\angle5=180^{\circ}-\angle2$. Substitute $\angle1 = 40^{\circ}$ and $\angle2 = 124^{\circ}$, we get $40^{\circ}+\angle5=180 - 124^{\circ}=56^{\circ}$, then $\angle5 = 16^{\circ}$.

Step3: Use corresponding - angle property

If we assume the two horizontal lines are parallel, $\angle5$ and $\angle7$ are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So $\angle7=\angle5 = 16^{\circ}$.

Answer:

$16$