Question

A quadrilateral has three acute angles, each measuring ${75}^o$. Find the measure of the fourth angle.

• A. ${65}^o$
• B. ${135}^o$
• C. ${140}^o$
• D. ${225}^o$

Answer 1

Answer: (B)

${135}^o$

Let the four angles be $\angle A,\angle B,\angle C$ and $\angle D$ .

Given $\angle A,\angle B,\angle C={75}^o$ .

We know, by angle sum property, the sum of angles of a quadrilateral is ${360}^o$.

$\angle A+\angle B+\angle C+\angle D={360}^o$.

Then, $\angle D$ will be given by:

$\angle D={360}^o-\angle A-\angle B-\angle C$

$\Rightarrow \angle D={360}^o-{75}^o-{75}^o-{75}^o$

$\Rightarrow \angle D=360-{225}^o$

$\Rightarrow \angle D={135}^o$.

The measure of fourth angle is ${135}^o$.

Therefore, option $B$ is correct.