Question

4. In the figure, AB || CD and PQ || RS. Find the values of x,y and z.
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Answer 1

Step-by-step explanation:

Given :

AB || CD

PQ || RS

Find :

< X

< Y

< Z

Solution :

AB || CD ( Given )

Since < ABE = ECD ( Alternate Interior Angel )

X = 40°

Similarly < BAE = < EDC

65° = Z

In ∆ BEA

< ABE + < BEA + < BAE = 180° ( Angle Sum

Of Propert )

< X + < Y + 65° = 180°

40° + < Y + 65° = 180°

< Y + 105° = 180°

< Y = 180° - 105°

< Y = 75°

The Value

< X = 40°

< Y = 75°

< Z = 65°

Here Are Some Important Properties

• Alternate Interior Angle = 180°
• Co - interior Angle = 180°
• Vertically opposite Angle = 180°

Answer 2

d:/

X = 90° , Y = 68°,z = 112°

Step-by-step explanation:

CDS = 180 - (22+90) = 68°

CDS = y° = 68° (opposite angles of a parallelogram are always equal)

Z = 180° - CDS = (180° - 68°) = 112°

x + y + (z-90°) = 180.

x + 68° + 22° = 180° => X = 90°