Question

In the given figure , AB||CD. Transversal L cuts AB and CD at P and Q respectively. Transversal m cuts AB and CD at R and S respectively. Find the value of x and also the measures of angle PQC and angle RSD.​

Answer 1

Solution:

From the figure, angle PRS = 4x

⠀⠀⠀⠀⠀⠀⠀[Vertically opposite angles]

and 4x + 5x = 180

⠀⠀[Co-interior angles are supplementary]

9x = 180

x = 180/9

x = 20°

angle PQC = 3x

[Corresponding angles axiom, AB||CD]

angle PQC = (3 x 20)° = 60°

and RSD = 4x

⠀ [Coresponding angles axiom, AB||CD]

angle RSD = (4 x 20°) = 80°

x = 20°,

angle PQC = 60° ,

angle RSD = 80°

Answer 2

Answer:



Step-by-step explanation: