Question

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

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). In a right - triangle, one angle is \(90^{\circ}\). So, \((4x - 5)+(3x - 3)+90=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(4x-5 + 3x-3+90=(4x + 3x)+(-5-3 + 90)=7x+82\). The equation becomes \(7x + 82=180\).

Step3: Solve for \(x\)

Subtract 82 from both sides: \(7x=180 - 82\), so \(7x=98\). Then divide both sides by 7: \(x=\frac{98}{7}\).

Answer:

\(x = 14\)