Three angles of a quadrilateral are 75°, 90° and 60°, the fourth angle is .

120°

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135°

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140°

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125°

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Solution

The correct option is B 135°
Let the fourth angle of the quadrilateral be x°.
By angle sum property, the sum of interior angles of a quadrilateral is 360°.
$\Rightarrow ∠ A + ∠ B + ∠ C + ∠ D = 360 °$
$\Rightarrow 75 ° + 90 ° + 60 ° + x ° = 360 °$
$\Rightarrow x ° = 360 ° - (75 ° + 90 ° + 60 °)$
$\Rightarrow x ° = 360 ° - 225 °$
$\Rightarrow x ° = 135 °$

Hence, the fourth angle of the quadrilateral is 135°.

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