A quadrilateral has three acute angles, each measuring 75°. Find the measure of the fourth angle.
135∘
Let the fourth angle be x∘.
We know that the sum of all the angles of a quadrilateral is 360∘.
Any angle measuring greater than 0∘ and less than 90∘ is an acute angle.
75∘+75∘+75∘+x=360
⇒225∘+x=360∘
⇒x=360∘–225∘
⇒x=135∘
Thus, the fourth angle is 135∘.