Answer:
112°
Step-by-step explanation:
Co-interior angles, also known as consecutive interior angles, are pairs of angles formed when two lines are intersected by a transversal. If the lines are parallel, then co-interior angles are supplementary, meaning they add up to 180 degrees.
Given: [tex] \angle 3 = 68^\circ [/tex]
Since [tex]\angle 3[/tex] and [tex]\angle 6[/tex] are co interior angles, so we can set up equation as:
[tex] \angle 3 + \angle 6 = 180^\circ [/tex]
[tex] 68^\circ + \angle 6 = 180^\circ [/tex]
[tex] \angle 6 = 180^\circ - 68^\circ [/tex]
[tex] \angle 6 = 112^\circ [/tex]
Vertically opposite angles are formed by the intersection of two lines. These angles are equal in measure.
since [tex]\angle 6[/tex] is vertically opposite to [tex]\angle 8[/tex]:
[tex] \angle 8 = \angle 6 = 112^\circ [/tex]
Therefore, the measure of [tex]\angle 8[/tex] is [tex]112^\circ[/tex].
