Question:
Three angles of a quadrilateral are 75°, 90° and 75°. Find the measure of the fourth angle.
Solution:
Given: Three angles of a quadrilateral are 75°, 90° and 75°.
Let the fourth angle be x.
Using angle sum property of quadrilateral,
$75^{\circ}+90^{\circ}+75^{\circ}+x=360^{\circ}$
$\Rightarrow 240^{\circ}+x=360^{\circ}$
$\Rightarrow x=360^{\circ}-240^{\circ}$
$\Rightarrow x=120^{\circ}$
So, the measure of the fourth angle is $120^{\circ}$.