Q76 of 93 Page 6

Three angles of a quadrilateral are respectively equal to 110°, 40° and 50°. Find the fourth angle.

Sum of the four angles of a quadrilateral = (2n - 4) right angles where n = 4
                                                        = (2 × 4 - 4) right angles
                                                        =  4 right angles
                                                        = 4 × 90°
                                                        = 360°
Sum of the three angles = 110° + 50° + 50° = 210°
∴ The fourth angle = 360° - 210° = 150°

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74 An exterior angle of a triangle is 115° and one of the interior opposite angles is 35°. Find the other two angles. 75 Can a triangle have
    (i) Two right angles?
    (ii) Two obtuse angles?
    (iii) Two acute angles
    (iv) All angles more than 60° ?
    (v) All angles less than 60° ?
    (vi) All angles equal to 60° ? 77 In figure, the bisectors of ∠ ABC and ∠ BCA intersect each other at O.Prove that ∠ BOC = 90°+∠ A. 
         78 In figure, the bisectors of the exterior angles at B and C formed by producing sides AB and AC of Δ ABC intersect each other at the point O. Prove that ∠ BOC=90° - ∠ A .