Question

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, 62°+20°+(6x + 18)°=180°.

Step2: Combine like - terms

First, add the constant angles: 62 + 20=82. The equation becomes 82+(6x + 18)=180. Then, combine 82 and 18: 82+18 + 6x=180, which simplifies to 100+6x=180.

Step3: Isolate the variable term

Subtract 100 from both sides of the equation: 6x=180 - 100. So, 6x=80.

Step4: Solve for x

Divide both sides by 6: x = $\frac{80}{6}=\frac{40}{3}=13\frac{1}{3}$.

Answer:

$x=\frac{40}{3}$