To find the missing angle measurement, we will use the Angle Sum Property to create an algebraic equation that can solve for a missing angle given two angles in a right triangle.
Create an Equation
We are given an angle of 27º and 90º (refer to the square in the bottom right-hand corner.
We know that all of the angles in a triangle must add up to 180º using the Angle Sum Property.
Create an equation to find the missing value.
[tex]27 + 90 + x = 180[/tex]
Combine Like Terms
Combine the constants on the left side of the equation.
[tex]27 + 90 + x = 180[/tex]
[tex]117 + x = 180[/tex]
Subtract
Subtract 117 from both sides of the equation.
[tex]117 - 117 + x = 180 - 117[/tex]
[tex]\boxed{x = 63}[/tex]
The final answer is x = 63º.
