Question

Seg XZ is a diameter of a circle. Point Y lies in its interior. How many of the following statements are true? 

(i) It is not possible that ∠XYZ is an acute angle. 

(ii) ∠XYZ can’t be a right angle. 

(iii) ∠XYZ is an obtuse angle. 

(iv) Can’t make a definite statement for measure of ∠XYZ. 

(A) Only one 

(B) Only two 

(C) Only three 

(D) All

Answer 1

(C) Only three

x. seg XZ is the diameter. 

∴ ∠XWZ is a right angle. [Angle inscribed in a semicircle]

Since, Y lies in the interior of ∆XWZ, 

∴ ∠XYZ > 90° 

i.e., ∠XYZ is an obtuse angle.