Question:
Three angles of a quadrilateral are $75^{\circ}, 90^{\circ}$ and $75^{\circ}$, then the fourth angle is
(a) $90^{\circ}$
(b) $95^{\circ}$
(c) $105^{\circ}$
(d) $120^{\circ}$
Solution:
(d) Given, ∠A = 75°, ∠B = 90° and ∠C = 75°
We know that, sum of all the1 angles of a quadrilateral is 360°.
∠A+ ∠B + ∠C + ∠D = 360°
=> 75° + 90°+ 75°+ ∠D = 360°
∠D = 360° – (75° + 90° + 75°)
= 360° -240° = 120°
Hence, the fourth angle of a quadrilateral is 120°.
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