Three angles of a quadrilateral are 75°, 90° and 75°.

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 $120^{\circ}$.

 

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