Question

Which of the following can be four interior angles of a quadrilateral?

• A. $140°,40°,20°,160°$
• B. $270°,150°,30°,20°$
• C. $40°,70°,90°,60°$
• D. $110°,40°,30°,180°$

Answer 1

Answer: (A), (D)

$110°,40°,30°,180°$

Step 1. Explanation for the correct option.

Sum of interior angles of a quadrilateral$=360°$

As,

$$\begin{gathered} 140°+40°+20°+160°=360° \\ 110°+40°+30°+180°=360° \end{gathered}$$

So, these angles can be four interior angles of a quadrilateral.

Step 2. Explanation for the incorrect options.

Since,

$$\begin{gathered} 270°+150°+30°+20°=470°\ne 360° \\ 40°+70°+90°+60°=260°\ne 360° \end{gathered}$$

Hence, the correct options are $A$ and $\mathrm{D}$.