In the figure, if AB ∥ CD, then find the value of ∠GHS.

In the figure, AB ∥ CD 

∠PRB = 2x ....... (Given)

As lines, AB and PQ intersect at R, ∠PRB =∠GRS 

⟹ ∠GRS = 2x ...(i)

As, ∠GRS + ∠HSR = 180^o ...... (Sum of the interior angle is supplementary)

∠HSR = 3x ....... (Given)

⟹ 2x + 3x = 180^o ..(from(i))

⟹ 5x = 180^o

⟹ x = 36^o 

As ∠EGA = 2x ........ (Given)

∠EGA + ∠EGR = 180^o ...(Supplementary Angles)

⟹ 2x + ∠EGR = 180^o 

⟹ ∠EGR = 180^o − 2x 

Also, ∠GHS = ∠EGR ....... (Corresponding angles are equal) 

⟹ ∠GHS = 180^o − 2x 

Putting a value of x = 36^o, we get:

∠GHS = 180^o −2 × 36 = 180^o − 72^o = 108^o

⟹ ∠GHS = 108^o