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When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.
<h3>What are Alternate exterior angles?</h3>When two parallel lines are cut by a transverse. the angles formed on the exterior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Exterior Angle.
Firstly, ∠1 and ∠7 are alternate exterior angles as shown in the image, now to prove if these two angles will be congruent we can use the below proof.
First Method:
∠1 + ∠2 = 180° {Supplementary angles because both lies on the line q}
∠2 = (180° - ∠1)
Similarly, ∠2 = ∠6 = (180° - ∠1), corresponding angles are equal,
∠6 + ∠7 = 180° {Supplementary angles because both lies on the line r}
∠7 = 180° - ∠6
∠7 = 180° - (180° - ∠1)
∠7 = 180° - 180° + ∠1
∠7 = ∠1
OR
Second Method:
∠1 = ∠3 {Vertical angles formed by intersecting lines q and r}
∠3 = ∠5 {Alternate Interior angles}
∠5 = ∠7 {Vertical angles formed by intersecting lines s and r}
Learn more about the Alternate Exterior Angles:
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