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, 40+(8x - 11)+90 = 180.

Step2: Simplify the left - hand side

Combine like terms: (40 + 90-11)+8x=180, which gives 119 + 8x=180.

Step3: Isolate the variable term

Subtract 119 from both sides: 8x=180 - 119, so 8x=61.

Step4: Solve for x

Divide both sides by 8: x = $\frac{61}{8}$ = 7.625.

Answer:

x = 7.625