Answer: [tex]m\angle 1=109\°\\m\angle 2=71\°[/tex]
Step-by-step explanation:
It is important to remember the definition of "Linear pair angles".
By definitiion "Linear pair angles" are two angles which are adjacents and supplementary.
Based on this, we know that the angles [tex]\angle1[/tex] and [tex]\angle2[/tex] are supplementary, which means that they add up to 180 degrees.
So, knowing that:
[tex]m\angle 1=5x+9\\m\angle 2=3x+11[/tex]
We can write the following expression and solve for "x":
[tex](5x+9)+(3x+11)=180\\\\8x=180-20\\\\x=\frac{160}{8}\\\\x=20[/tex]
Therefore, substituting, we get that the measures of the angles [tex]\angle1[/tex] and [tex]\angle2[/tex] are:
[tex]m\angle 1=5(20)+9=109\°\\\\\\m\angle 2=3(20)+11=71\°[/tex]
