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Describing Triangles

Describing Triangles 1.13 - Solution

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We want to find the measure of each acute angle.

To do this, we will first find the value of xx by using the interior angles theorem. This theorem tells us that the measures of the interior angles of a triangle add to 180.180^\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 90.90^\circ. (x+11)+(3x9)+90=180 (x+11)+(3x-9)+90=180 We will now solve the equation for x.x.
(x+11)+(3x9)+90=180(x+11)+(3x-9)+90=180
Solve for xx
x+11+3x9+90=180x+11+3x-9+90=180
4x+92=1804x+92=180
4x=884x=88
x=22x=22
Now that we know the value of x,x, we can substitute x=22x=\textcolor{darkviolet}{22} into the given expressions to find the measures of the acute angles. x+113(22+11= 333x93(22)9= 57\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}