Answer:
[tex]x=22\text{ and } y=123[/tex]
Step-by-step explanation:
By definition, the interior angles of a triangle must sum to 180°. Therefore:
[tex](2x+13)+(57)+(3x)=180[/tex]
Combine like terms:
[tex]5x+70=180[/tex]
Subtract 70 from both sides:
[tex]5x=110[/tex]
And divide both sides by five. Hence:
[tex]x=22[/tex]
Next, notice that y and the 57° angle form a linear pair. By definition, linear pairs equal 180°. Therefore:
[tex]y+57=180[/tex]
So:
[tex]y=123[/tex]
Alternatively, we can use the Exterior Angle Theorem, which states that the exterior angle is equivalent to the sum of the two interior angles opposite to the exterior angle. In other words:
[tex]y=(2x+13)+(3x)[/tex]
Since we've determined that x = 22:
[tex]y=(2(22)+13)+(3(22))=44+13+66= 123[/tex]
We acquire the same answer.
