Question

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

• A. ${225}^{\circ }$
• B. ${100}^{\circ }$
• C. ${140}^{\circ }$
• D. ${135}^{\circ }$

Answer 1

The correct option is D

${135}^{\circ }$

Let the fourth angle be $x^{\circ }$.

We know that the sum of all the angles of a quadrilateral is ${360}^{\circ }$.

Any angle measuring greater than $0^{\circ }$ and less than ${90}^{\circ }$ is an acute angle.

${75}^{\circ }+{75}^{\circ }+{75}^{\circ }+x=360$

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

$\Rightarrow x={360}^{\circ }–{225}^{\circ }$

$\Rightarrow x={135}^{\circ }$

Thus, the fourth angle is ${135}^{\circ }$.