Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the given triangle, the angles are 90°, 23°, and (8x + 3)°. So, 90+23+(8x + 3)=180.

Step2: Simplify the left - hand side of the equation

Combine like terms: 90+23 + 3+8x=180, which simplifies to 116+8x=180.

Step3: Isolate the variable term

Subtract 116 from both sides of the equation: 8x=180 - 116. So, 8x=64.

Step4: Solve for x

Divide both sides by 8: x = \frac{64}{8}=8.

Answer:

8