Question

find the measure of angles 1 - 7 given that lines m and n are parallel and t is transversal. m∠1 = □°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle adjacent to the $40^{\circ}$ angle and $\angle1$ are vertical angles. So $m\angle1 = 40^{\circ}$.

Step2: Use corresponding - angle property for other angles

Since lines $m$ and $n$ are parallel and $t$ is a transversal:

• $\angle2$ and the $40^{\circ}$ angle are corresponding angles, so $m\angle2=40^{\circ}$.
• $\angle3$ and the $40^{\circ}$ angle are vertical angles, so $m\angle3 = 40^{\circ}$.
• $\angle4$ and $\angle2$ are vertical angles, so $m\angle4=40^{\circ}$.
• $\angle5$ and the $40^{\circ}$ angle are alternate - interior angles, so $m\angle5 = 40^{\circ}$.
• $\angle6$ and $\angle5$ are vertical angles, so $m\angle6=40^{\circ}$.
• $\angle7$ and $\angle4$ are alternate - interior angles, so $m\angle7 = 40^{\circ}$.

Answer:

$m\angle1 = 40^{\circ}$, $m\angle2 = 40^{\circ}$, $m\angle3 = 40^{\circ}$, $m\angle4 = 40^{\circ}$, $m\angle5 = 40^{\circ}$, $m\angle6 = 40^{\circ}$, $m\angle7 = 40^{\circ}$