1 Answer

Riiich · Answer 1 · 2023-08-15T04:03:51+0000

Answer:

$\angle3=33º$

Step-by-step explanation:

If two angles are supplentary, their sum is equal to 180º

If two angles are complementary, their sum is equal to 90º

We know:

$\begin{gathered} \angle1=(8x+3)º \\ \angle2=(5x-18)º \end{gathered}$

Also,

$\begin{gathered} \angle1+\angle2=180º \\ \angle2+\angle3=90º \end{gathered}$

Now, we can write:

$\operatorname{\angle}1+\operatorname{\angle}2=180\Rightarrow(8x+3)+(5x-18)=180$

And solve for x:

$\begin{gathered} 8x+3+5x-18=180 \\ 13x-15=180 \\ 13x=180+15 \\ . \\ x=(195)/(13) \\ . \\ x=15 \end{gathered}$

Now we can find the measure of angle 2:

$\angle2=(5x-18)º\Rightarrow\angle2=(5\cdot15-18)º=(75-18)º=57º$

And since angle 2 and 3 are complementary:

$\angle2+\angle3=90º\Rightarrow57º+\angle3=90º$

And solve:

$\begin{gathered} 57º+\angle3=90º \\ \angle3=90º-57º \\ \angle3=33º \end{gathered}$

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