To solve this problem, you will first use the Angle Sum Property to determine the value of x after creating an algebraic equation, combining like terms, and subtracting from both sides of an equation.
Use the Angle Sum Property
The Angle Sum Property states that all interior angles of a triangle will summate to 180º.
An equation can be created to find this when you are given two angles and missing a third. That third angle can be referred to as x in this scenario.
Adding the two known angles and the unknown angle will result in a sum of 180º. This means that our unknown is x and can therefore be placed in an equation:
[tex]65+42+x=180[/tex]
Combine Like Terms
Combine the like terms by combining the constants on the left side of the equation using addition:
[tex]65+42+x=180[/tex]
[tex]107+x=180[/tex]
Subtract
After combining like terms, subtract 107 from both sides of the equation:
[tex]107 - 107 +x = 180-107[/tex]
[tex]\boxed{x=73}[/tex]
The final answer is x = 73 degrees.
