Question

AB ll CD, Find the value of x with exterior angle property​

Answer 1

Step-by-step explanation:

Given that AB∣∣CD

Taking PQ as transversal,

∠RQP=∠QPC=80

∘

Now,

∠QPC+2x+3x=180

∘

80

∘

+5x=180

∘

5x=130

∘

x=26

∘

now, applying angle sum property in triangle PQR,

2x+y+∠PQR=180

∘

2×26+80

∘

+y=180

∘

y=48

∘

now,

z=2x+80

∘

(An exterior angle of a triangle is equal to the sum of the opposite interior angles)

z=2×26

∘

+80

∘

=52

∘

+80

∘

=132

∘

z=132

∘