Question

question 11 (3 points) find m∠1, m∠2 and m∠3. complete the reasoning: m∠1 = 100 ° is a angle with the given. m∠2 = ° is a angle with ∠1 m∠3 = ° is a angle with ∠2

Explanation:

Step1: Identify vertical - angle relationship

$\angle1$ and the given $80^{\circ}$ angle are supplementary. Since supplementary angles add up to $180^{\circ}$, $m\angle1 = 180 - 80=100^{\circ}$. $\angle1$ is a supplementary angle with the given $80^{\circ}$ angle.

Step2: Identify corresponding - angle relationship

$\angle2$ and $\angle1$ are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal. So $m\angle2 = 100^{\circ}$. $\angle2$ is a corresponding angle with $\angle1$.

Step3: Identify vertical - angle relationship

$\angle3$ and $\angle2$ are vertical angles. Vertical angles are equal. So $m\angle3 = 100^{\circ}$. $\angle3$ is a vertical angle with $\angle2$.

Answer:

Blank 1: 100
Blank 2: 100
Blank 3: corresponding
Blank 4: 100
Blank 5: vertical