This is an important ques from circles, ml aggarwal, chapter 15, angle properties or circle,

we have been given a circle based question, and we are asked the value of x in this figure, using the properties of circles

ML Aggarwal solution, class10th, understanding ICSE mathematics

∠DAB = ∠BCD

(Angles in the same segment of the circle)

∠DAB = 25

^{0}(∠BCD = 25^{0 }given)In ∆DAP,

Ex, ∠CDA = ∠DAP + ∠DPA

x

^{o }= ∠DAB + ∠DPAx

^{o }= 25^{o }+ 35^{o}x

^{o }= 60^{o}