Question

use the diagram to find the angle measures. complete the reasoning: m∠3 = __° because ∠3 and the given are angles m∠2 = ° because ∠2 and the given are angles m∠1 = 80 ° because ∠1 and ∠2 are __ angles

Explanation:

Step1: Identify vertical - angle relationship

$\angle3$ and the $100^{\circ}$ angle are vertical angles. Vertical angles are equal. So $m\angle3 = 100^{\circ}$.

Step2: Identify corresponding - angle relationship

$\angle2$ and the $100^{\circ}$ angle are corresponding angles. When lines are parallel, corresponding angles are equal. So $m\angle2=100^{\circ}$.

Step3: Identify supplementary - angle relationship

$\angle1$ and $\angle2$ are supplementary angles (since they form a linear - pair). Supplementary angles add up to $180^{\circ}$. Given $m\angle2 = 100^{\circ}$, then $m\angle1=180 - 100=80^{\circ}$.

Answer:

Blank 1: 100
Blank 2: 100
Blank 3: vertical
Blank 4: corresponding
Blank 5: 80
Blank 6: supplementary