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  • If three angles of a quadrilateral are 75º, 90º and 75º then find the fourth angle (A) 90º (B) 95º (C) 105º (D) 120º

If three angles of a quadrilateral are 75^{\circ}, 90^{\circ} and 75^{\circ} then find the fourth angle
(A) 90^{\circ}        (B) 95^{\circ}   (C) 105^{\circ}          (D) 120^{\circ}

Answers (1)

Answer:    [D]   120^{\circ}

Solution.
As we know that the sum of the angles of a quadrilateral is 360^{\circ}.
i.e., \angle 1+\angle 2+\angle 3+\angle 4=360^{\circ}           …..(i)

Here    \angle 1=75^{\circ} 
            \angle 2=90^{\circ}
            \angle 3=75^{\circ}
Put the values in equation (i) we get
75^{\circ}+90^{\circ}+75^{\circ}+\angle 4=360^{\circ}
\angle 4=360^{\circ}-240^{\circ}
\angle 4=120^{\circ}
Hence option D is correct.

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infoexpert26

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