A quadrilateral has three acute angles each measuring 75°. Find the measure of the fourth angle.

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120°

135°

105°

140°

answer is A.

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Detailed Solution

Let the four angles be ∠A, ∠B, ∠C, and ∠D.

Given ∠A, ∠B, ∠C = 75^o

We know, by angle sum property, the sum of angles of a quadrilateral is 360°

∠A + ∠B + ∠C + ∠D = 360°

Then, ∠D will be given by:

∠D = 360° − ∠A − ∠B − ∠C

⇒ ∠D = 360° − 75° − 75° − 75°

⇒ ∠D = 360 − 225°

⇒ ∠D = 135°

Thus, The measure of the fourth angle is 135°.

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