In ΔPQS, 110∘+∠1=180∘ ⇒∠1=180∘−110∘ [linear pair of angles] ⇒∠1=70∘
Also, ∠1=∠2=70∘ [∵ PQ = PS]
Angles opposite equal sides are equal.
As we know, the measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles ∴∠2=x+25∘ ⇒70∘=x+25∘ [∵∠2=70∘] ⇒x=70∘−25∘⇒x=45∘