Question

4 fill in the blank 1 point find the missing angle: the type of the two given angles is choose your answer... therefore, they are choose your answer... and the missing angle is choose your answer...

Explanation:

Step1: Identify angle relationship

The two lines are parallel, cut by a transversal. The given angle (112°) and the missing angle are same - side interior angles? Wait, no, looking at the diagram, actually, the two angles (112° and the missing one) are same - side interior angles? Wait, no, wait. Wait, when two parallel lines are cut by a transversal, same - side interior angles are supplementary. Wait, but let's check the positions. Wait, the two angles: one is 112°, the other is adjacent? Wait, no, the two angles formed by the transversal and the parallel lines. Wait, actually, the two angles (112° and the missing angle) are same - side interior angles? Wait, no, let's recall: same - side interior angles are supplementary (sum to 180°). Wait, but wait, maybe they are consecutive interior angles. Wait, the formula for consecutive interior angles (same - side interior angles) is that they are supplementary. So if one angle is 112°, the other should be 180 - 112.

Step2: Calculate the missing angle

We know that for two parallel lines cut by a transversal, same - side interior angles are supplementary, i.e., their sum is 180°. Let the missing angle be \( x \). Then we have the equation:
\( 112^{\circ}+x = 180^{\circ} \)
To find \( x \), we subtract 112° from both sides:
\( x=180^{\circ}- 112^{\circ} \)
\( x = 68^{\circ} \)

Answer:

The type of the two given angles is same - side interior angles (consecutive interior angles), they are supplementary, and the missing angle is \( 68^{\circ} \). (If we consider the dropdowns: first dropdown: same - side interior angles; second dropdown: supplementary; third dropdown: 68°)