Answer :
Answer:
[tex]\boxed {\angle 1 = 45\textdegree}[/tex]
Step-by-step explanation:
First you need to write an expression by using the following equations from both [tex]\angle 1[/tex] and [tex]\angle 2[/tex] and solve for [tex]x[/tex]:
[tex]\angle 1 = 2x + 13[/tex]
[tex]\angle 2 = 8x - 83[/tex]
[tex]2x + 13 = 8x - 83[/tex]
-Solve:
[tex]2x + 13 = 8x - 83[/tex]
[tex]2x + 13 - 8x = 8x - 8x - 83[/tex]
[tex]-6x + 13 = -83[/tex]
[tex]-6x + 13 - 13 = -83 - 13[/tex]
[tex]-6x = -96[/tex]
[tex]\frac{-6x}{-6} = \frac{-96}{-6}[/tex]
[tex]x = 16[/tex]
After you have found the value of [tex]x[/tex], you need to apply the value of [tex]x[/tex] to the equation of [tex]\angle 1[/tex] and solve for the measurement of [tex]\angle 1[/tex]:
-The value of [tex]x[/tex]:
[tex]x = 16[/tex]
-Solve for the measurement of [tex]\angle 1[/tex]:
[tex]2x + 13[/tex]
[tex]2(16) + 13[/tex]
[tex]32 + 13[/tex]
[tex]45\textdegree[/tex]
-The measurement of [tex]\angle 1[/tex]:
[tex]\boxed {\angle 1 = 45\textdegree}[/tex]