Question

A quadrilateral has three acute angles, each measuring 45${}^{\circ }$. Find the measure of the fourth angle.

• A. 225${}^{\circ }$
• B. 245${}^{\circ }$
• C. 235${}^{\circ }$
• D. 275${}^{\circ }$

Answer 1

The correct option is A 225${}^{\circ }$

Sum of the four angles of a quadrilateral is 360${}^{\circ }$.

If the unknown angle is x${}^{\circ }$,

$\Rightarrow$ 45${}^{\circ }$ + 45${}^{\circ }$ + 45${}^{\circ }$ + x${}^{\circ }$ = 360${}^{\circ }$
$\Rightarrow$ x${}^{\circ }$ = 360${}^{\circ }$ − 135${}^{\circ }$
$\Rightarrow$ = 225${}^{\circ }$

Hence, the fourth angle measures 225${}^{\circ }$.