Question

13 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 type

The two lines are parallel, cut by a transversal. The angles are corresponding angles (or alternate interior/exterior, but here corresponding as they are in same relative position). Corresponding angles are equal when lines are parallel.

Step2: Determine angle relation

Since they are corresponding angles, they are equal.

Step3: Find missing angle

Given one angle is \(80^\circ\), the missing angle (corresponding) is also \(80^\circ\)? Wait, no—wait, maybe alternate interior? Wait, the angle given is \(80^\circ\), and the missing angle: wait, maybe the angle and the \(80^\circ\) are corresponding, so equal. Or maybe vertical? Wait, no, the diagram: two parallel lines, transversal. The angle marked \(80^\circ\) and the missing angle—if they are corresponding, then equal. Wait, maybe the angle is \(80^\circ\) or \(100^\circ\)? Wait, no, let's re-examine. If the angle is adjacent to a straight line, but no—wait, the two angles: the given \(80^\circ\) and the missing angle. If they are corresponding angles (same position relative to parallel lines and transversal), then they are equal. So the type is corresponding angles, they are equal, so missing angle is \(80^\circ\). Wait, but maybe I made a mistake. Wait, no—if the angle is on the same side, corresponding, so equal. So:

The type of the two given angles is corresponding angles (or alternate, but corresponding is more likely). Therefore, they are equal, and the missing angle is \(80^\circ\). Wait, but maybe the angle is supplementary? No, parallel lines cut by transversal: corresponding angles equal, alternate interior equal, consecutive interior supplementary. Wait, maybe the given angle is \(80^\circ\), and the missing angle is equal (corresponding) or supplementary? Wait, no, let's draw mentally: two horizontal parallel lines, transversal. The lower angle is \(80^\circ\) (between transversal and lower parallel line, left side). The upper angle (between transversal and upper parallel line, left side) would be corresponding, so equal. So yes, \(80^\circ\).

Answer:

The type of the two given angles is \(\boldsymbol{\text{corresponding angles}}\). Therefore, they are \(\boldsymbol{\text{equal}}\) and the missing angle is \(\boldsymbol{80^\circ}\).