We can use the given algebraic expressions for the angle measures of a triangle to find the numeric measures of these angles.
2x, x+24, x-4
The Triangle Angle Sum Theorem tells us that the sum of the angle measures of any triangle will be 180^(∘).
m ∠ A+m ∠ B+m ∠ C=180
Applying this theorem, we can write an equation for the sum of the angle measures of our triangle.
(2x)+(x+24)+(x-4)=180
Now, let's solve this equation for x.
The value of x is 40. Next, we can substitute 40 for x into the algebraic expressions to find the angle measures for our triangle.
ccccc
Expression & & x= 40 & &Angle [0.5em]
2x & ⇒ & 2( 40) & ⇒ &80
x+24 & ⇒ & 40+24 &⇒ &64
x-4 & ⇒ & 40-4 &⇒ &36
We can check our answer by substituting the angle measures into the equation created by the Triangle Angle Sum Theorem.
