Question

find m∠1 and m∠2. complete the reasoning: m∠2 = ____° is a __ angle with the given. m∠1 = __° is a ____ angle with ∠2.

Explanation:

Step1: Identify angle - relationship for $\angle2$

Since $\angle2$ and the given $66^{\circ}$ angle are corresponding angles (formed by a transversal intersecting two parallel lines $\overleftrightarrow{MP}$ and $\overleftrightarrow{NL}$), $m\angle2 = 66^{\circ}$.

Step2: Identify angle - relationship for $\angle1$

$\angle1$ and $\angle2$ are same - side interior angles (formed by a transversal intersecting two parallel lines $\overleftrightarrow{MP}$ and $\overleftrightarrow{NL}$). The sum of same - side interior angles is $180^{\circ}$. So $m\angle1=180 - 66=114^{\circ}$.

Answer:

Blank 1: 66
Blank 2: corresponding
Blank 3: 114
Blank 4: same - side interior