Question

A quadrilateral has three acute angles. If each measures $80°$, then the measure of the fourth angle is

• A. $150°$
• B. $120°$
• C. $105°$
• D. $140°$

Answer 1

The correct option is B

$120°$

Explanation for the correct otpion:

Finding the fourth angle:

From the angle sum property of a quadrilateral, we know that the sum of the interior angles of a quadrilateral is equal to $360°$.

Let us assume the fourth angle be $n$

Then,

$$\begin{gathered} 80°+80°+80°+n=360° \\ \Rightarrow 240°+n=360° \\ \Rightarrow n=360°–240° \\ \Rightarrow n=120° \end{gathered}$$

Thus, the measure of fourth angle is $120°$

Hence, the correct option is (B).