Question

Fill in the blanks with acute, obtuse, right or straight:

When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be __________.

Answer 1

Define obtuse angles

An obtuse angle is the one whose measure is more than $90°$ but less than $180°$, while a straight angle is the one who measure is equal to $180°$. Also, an acute angle is the one who measure is less than $90°$.

So, to form a straight angle, if one angle added is acute, then the other has to be an obtuse angle.

For example: Consider an acute angle $50°$ (angle less than $90°$). Now let the other angle be $x°$. Upon adding these two the result will be $180°$, so the measure of $x$ will be

$$\begin{gathered} \Rightarrow x+50=180° \\ \Rightarrow x=180-50 \\ \Rightarrow x=130° \end{gathered}$$

Here, $x$ is less than $180°$ but more than $90°$, which forms an obtuse angle.

Therefore, when the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be an obtuse angle.