Question

the measures of the angles of a triangle are shown in the figure below. solve for x.

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So, $(3x + 4)+(3x-19)+45=180$.

Step2: Combine like - terms

First, combine the x - terms and the constant terms: $(3x+3x)+(4 - 19+45)=180$, which simplifies to $6x+( - 15 + 45)=180$, and further to $6x + 30=180$.

Step3: Isolate the variable term

Subtract 30 from both sides of the equation: $6x+30 - 30=180 - 30$, resulting in $6x=150$.

Step4: Solve for x

Divide both sides by 6: $\frac{6x}{6}=\frac{150}{6}$, so $x = 25$.

Answer:

25