Answer:
∠1 → 108
∠2 → 72
Step-by-step explanation:
Supplementary angles add up to a total of 180° (two angles is a pair). So:
∠1+∠2=180°
∠1 → supplement
∠2 → 36 less than the supplement
Create an equation, using x as angle 1 and y as angle 2:
[tex]x+y=180[/tex]
Insert the given values:
[tex]x+(x-36)=180[/tex]
Solve for the value of x. Simplify parentheses:
[tex]x+x-36=180[/tex]
Simplify addition:
[tex]2x-36=180[/tex]
Add 36 to both sides:
[tex]2x-36+36=180+36\\\\2x=216[/tex]
Isolate the variable. Divide both sides by 2:
[tex]\frac{2x}{2}=\frac{216}{2}\\\\ x=108[/tex]
The value of x is 108. Insert this into the equation above:
[tex]x+y=180\\\\108+y=180[/tex]
Solve for y. Subtract 108 from both sides:
[tex]108-108+y=180-108\\\\y=72[/tex]
The value of y is 72.
Therefore:
∠1 → 108
∠2 → 72
:Done
*Check:
Insert the values into an equation set to 180 to determine if true:
[tex]108+72=180\\\\180=180[/tex]
Subtract 108 by 72 to see if the difference is 36:
[tex]108-72=36\\36=36[/tex]
The given values are true.
