One angle of a cyclic quadrilateral is given. Find the opposite angle.

(i) 70° (ii) 135°

(iii) (iv) right angle

(iv) 165°

We know that the pair of opposite angles of a cyclic quadrilateral is supplementary i.e. sum is 180°.

Let the opposite angle of the cyclic quadrilateral be x°.

(i) Given angle = 70°

⇒ 70° + x° = 180°

⇒x° = 180° - 70°

∴ x° = 110°

(ii)Given angle = 135°

⇒ 135° + x° = 180°

⇒x° = 180° - 135°

∴ x° = 45°

(iii)Given angle = 1121/2°

⇒ 1121/2° + x° = 180°

⇒x° = 180° - 1121/2°

∴ x° = 671/2°

(iv)Given angle = right angle

⇒ 54° + x° = 180°

⇒x° = 180° - 54°

∴ x° = 126°

(v) Given angle = 165°

⇒ 165° + x° = 180°

⇒x° = 180° - 165°

∴ x° = 15°