In the figure a//b and both lines are intersected by transversal t. Complete the statements to prove that and are supplementary angles.

Alternate exterior angles are ones that are outside the "block" formed by the parallel lines and on opposite sides of the transversal. Both ∠2 and ∠7 are outside the parallel lines; additionally, ∠2 is on the right side of the transversal and ∠7 is on the left. This makes them alternate exterior angles.

A linear pair is a pair of angles that form a straight line. ∠7 and ∠8, when combined, form a straight line; this makes them a linear pair.

divyamadaan8054 divyamadaan8054 · Answer 2 · 2021-10-19T11:23:49+02:00

Hence, [tex]\angle 2\; \&\; \angle 8[/tex] are supplementary angles as [tex]\angle 2+\angle8=180^\circ[/tex].

Explanation:

Given: [tex]a\parallel b[/tex] and both lines are intersected by transversal [tex]t[/tex].

From the figure,

[tex]a\parallel b\\[/tex] (Given)

[tex]\angle 2=\angle 7\\[/tex] (Alternate Exterior opposite angles)

[tex]\angle 7+\angle8=180^\circ[/tex] (Linear pair property)

[tex]\angle 2+\angle8=180^\circ[/tex] (Co-exterior angles)

Here, [tex]\angle 2\; \&\; \angle 8[/tex] are supplementary angles as sum of these two angles are equal to [tex]180^\circ[/tex].

Therefore, [tex]\angle 2\; \&\; \angle 8[/tex] are supplementary angles as [tex]\angle 2+\angle8=180^\circ[/tex].

Hence proved.

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