Question

If three angles of a quadrilateral are each equal to ${75}^{\circ }$, then the fourth angle is

• A. ${150}^{\circ }$
• B. ${135}^{\circ }$
• C. ${45}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B

${135}^{\circ }$

Explanation for correct option
Given that three angles of a quadrilateral are each equal to ${75}^{\circ }$

Let the fourth angle of a quadrilateral is $\text{'}x\text{'}$
We know that sum of interior angles of a quadrilateral $={360}^{\circ }$
$$\begin{gathered} \Rightarrow 3\times {75}^{\circ }+x={360}^{\circ } \\ \Rightarrow {225}^{\circ }+x={360}^{\circ } \\ \Rightarrow x={360}^{\circ }-{225}^{\circ } \\ \hspace{0.17em}={135}^{\circ } \end{gathered}$$

Hence option(B) i.e. ${135}^{\circ }$ is correct.