Question

If three angles of a quadrilateral are $110°$, $65°$ and $105°$, then find the measure of the fourth angle.

Answer 1

Finding the fourth angle of the given quadrilateral.

Given: Three angles of a quadrilateral are $110°$, $65°$ and $105°$.

We know that the sum of angles of a quadrilateral is $360°$.

Let the fourth angle be x.

Therefore,

$$\begin{gathered} 110°+65°+105°+x=360° \\ \Rightarrow 280°+x=360° \\ \Rightarrow x=360°-280° \\ \Rightarrow x=80° \end{gathered}$$

Hence, the measure of the fourth angle is $80°$.