Question

the measures of the angles of a triangle are shown in the figure below. solve for x. 33° (5x - 13)°

Explanation:

Step1: Sum of triangle angles

The sum of angles in a triangle is $180^\circ$. The triangle has a right angle ($90^\circ$), $33^\circ$, and $(5x-13)^\circ$. Set up the equation:
$$90 + 33 + (5x - 13) = 180$$

Step2: Simplify left side

Combine constant terms:
$$90 + 33 - 13 + 5x = 180$$
$$110 + 5x = 180$$

Step3: Isolate the variable term

Subtract 110 from both sides:
$$5x = 180 - 110$$
$$5x = 70$$

Step4: Solve for x

Divide both sides by 5:
$$x = \frac{70}{5}$$

Answer:

$x = 14$