Question

In the adjoining figure if AB // CD then find x, y, z.
Ce
P
3x
23
►D
As
180
►B
Q
R​

Answer 1

Given,

AB II CD

PQR is a triangle ️.

To find : x, y, z

Solution : Since AB II CD,

Thus,

Angle DPQ + Angle RQP = 180⁰

( Sum of co-intererior angles on the same side of transversal in a parallel lines is 180⁰)

=> 2x⁰ + 3x⁰ + 80⁰ = 180⁰

=> 5x⁰ = 180⁰ - 80⁰

100

100=> x = ------ = 20⁰

100=> x = ------ = 20⁰ 5

Thus, Angle QPR = 2x = 40

in triangle PQR,

ANGLE (PQR +QPR+RPQ) = 180⁰

( angle sum property)

=> 80⁰ + y⁰ + 40⁰ = 180⁰

=> y⁰ + 120⁰ = 180⁰

=> y⁰ = 180⁰ - 120⁰ = 60⁰

Now,

y⁰ + z⁰ = 180⁰ ( linear pair)

thus, 60⁰ + z⁰ = 180⁰

thus, z = 180 - 60 = 120⁰