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 angles in a triangle is 180°. So, \(33^{\circ}+90^{\circ}+(5x - 13)^{\circ}=180^{\circ}\).

Step2: Combine like - terms

First, add the known angles: \(33 + 90=123\). The equation becomes \(123+(5x - 13)=180\). Then simplify the left - hand side: \(123+5x-13 = 5x + 110\). So, \(5x+110 = 180\).

Step3: Isolate the variable term

Subtract 110 from both sides of the equation: \(5x+110 - 110=180 - 110\). This gives \(5x=70\).

Step4: Solve for x

Divide both sides by 5: \(\frac{5x}{5}=\frac{70}{5}\). So, \(x = 14\).

Answer:

\(x = 14\)