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# Describing Triangles

## Describing Triangles 1.13 - Solution

We want to find the measure of each acute angle.

To do this, we will first find the value of $x$ by using the interior angles theorem. This theorem tells us that the measures of the interior angles of a triangle add to $180^\circ.$ Let's create an equation applying this theorem. Be aware that one of the angles is marked as a right angle, and therefore it measures $90^\circ.$ $(x+11)+(3x-9)+90=180$ We will now solve the equation for $x.$
$(x+11)+(3x-9)+90=180$
Solve for $x$
$x+11+3x-9+90=180$
$4x+92=180$
$4x=88$
$x=22$
Now that we know the value of $x,$ we can substitute $x=\textcolor{darkviolet}{22}$ into the given expressions to find the measures of the acute angles. \begin{aligned} x+11 \quad\Rightarrow\quad & \phantom{3(} \textcolor{darkviolet}{22}+11 &= \ 33 \\ 3x-9 \quad\Rightarrow\quad &3(\textcolor{darkviolet}{22})-9 &= \ 57\\ \end{aligned}