Question

1. complete the two problems below by filling out the missing angle. then fill in the blanks with the correct vocabulary using the vocabulary bank; not all words will be used. vocab bank: supplementary, complementary, alternate interior, corresponding, vertical, alternate exterior ∠1 = __ ∠2 = 58° ∠3 = 122° ∠4 = ∠1 and ∠3 are angles. ∠1 and ∠2 are angles. ∠4 and ∠2 are angles. ∠4 and ∠3 are __ angles.

Explanation:

Step1: Identify angle - pair relationships

Given $\angle2 = 58^{\circ}$ and $\angle3=122^{\circ}$. Since $\angle1$ and $\angle2$ form a straight - line, $\angle1+\angle2 = 180^{\circ}$.

Step2: Calculate $\angle1$

$\angle1=180^{\circ}-\angle2=180 - 58=122^{\circ}$

Step3: Calculate $\angle4$

$\angle4$ and $\angle2$ are corresponding angles (for parallel lines cut by a transversal), so $\angle4=\angle2 = 58^{\circ}$

Step4: Determine angle - pair types

$\angle1$ and $\angle3$ are vertical angles (opposite angles formed by the intersection of two lines), $\angle1$ and $\angle2$ are supplementary angles ($\angle1+\angle2 = 180^{\circ}$), $\angle4$ and $\angle2$ are corresponding angles, $\angle4$ and $\angle3$ are alternate exterior angles.

Answer:

$\angle1 = 122^{\circ}$
$\angle4 = 58^{\circ}$
$\angle1$ and $\angle3$ are vertical angles
$\angle1$ and $\angle2$ are supplementary angles
$\angle4$ and $\angle2$ are corresponding angles
$\angle4$ and $\angle3$ are alternate exterior angles