Answer:
[tex]\angle3=33º[/tex]
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:
[tex]\begin{gathered} \angle1=(8x+3)º \\ \angle2=(5x-18)º \end{gathered}[/tex]
Also,
[tex]\begin{gathered} \angle1+\angle2=180º \\ \angle2+\angle3=90º \end{gathered}[/tex]
Now, we can write:
[tex]\operatorname{\angle}1+\operatorname{\angle}2=180\Rightarrow(8x+3)+(5x-18)=180[/tex]
And solve for x:
[tex]\begin{gathered} 8x+3+5x-18=180 \\ 13x-15=180 \\ 13x=180+15 \\ . \\ x=\frac{195}{13} \\ . \\ x=15 \end{gathered}[/tex]
Now we can find the measure of angle 2:
[tex]\angle2=(5x-18)º\Rightarrow\angle2=(5\cdot15-18)º=(75-18)º=57º[/tex]
And since angle 2 and 3 are complementary:
[tex]\angle2+\angle3=90º\Rightarrow57º+\angle3=90º[/tex]
And solve:
[tex]\begin{gathered} 57º+\angle3=90º \\ \angle3=90º-57º \\ \angle3=33º \end{gathered}[/tex]
