Question

question 11 10 pts the angles of a triangle are represented by the expressions 2x + 10°, 3x - 5°, and x + 15°. what is the value of x?

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is $180^{\circ}$. So, we set up the equation $(2x + 10)+(3x - 5)+(x + 15)=180$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $(2x+3x + x)+(10 - 5+15)=180$, which simplifies to $6x+20 = 180$.

Step3: Isolate the variable term

Subtract 20 from both sides of the equation: $6x=180 - 20$, so $6x=160$.

Step4: Solve for $x$

Divide both sides by 6: $x=\frac{160}{6}=\frac{80}{3}=26\frac{2}{3}$.

Answer:

$x = \frac{80}{3}$