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The Z - shape stands for alternate angles.

t

t t

Knowledge Desk
The Indus Valley Civilization (IVC), which flourished in present-day
India and Pakistan around 2500 BCE, is renowned for its remarkable
town planning. A key feature of their cities, such as Mohenjo-daro and
Harappa was the use of straight streets that almost always intersected
at right angles (90 degrees), creating a grid-like pattern. This advanced
layout demonstrates the early use of geometry in urban design, where
streets acted as transversal lines cutting through parallel avenues. The
thoughtful arrangement not only allowed for efficient movement but
also ensured better water drainage and sanitation.

Example 8: In the following figure, XY cuts two parallel lines AB and CD at two points E and F
respectively.

If ∠1 = 100°, find all other angles. X
E
Solution: Given, ∠1 = 100° 2 ∠1 = 100°
A 3 4 B
Since, ∠1 and ∠2 makes a linear pair of angles.

\ ∠1 + ∠2 = 180° 6 F
5
100° + ∠2 = 180° C 7 8 D

∠2 = 180° – 100° Y
∠2 = 80°
Also, ∠3 = ∠1 (Vertically opposite angles)

\ ∠3 = 100°
Now, ∠4 = ∠2 = 80° (Vertically opposite angles)

∠5 = ∠3 = 100° (Pair of Alternate angles)
∠6 = ∠4 = 80° (Pair of Alternate angles)

∠7 = ∠5 = 100° (Vertically opposite angles)
∠8 = ∠6 = 80° (Vertically opposite angles)

Therefore, we have the following measurements:

∠1 = 100°, ∠2 = 80°, ∠3 = 100°, ∠4 = 80°
∠5 = 100°, ∠6 = 80°, ∠7 = 100°, ∠8 = 80°

157 Lines and Angles