Question

what is the value of x? s x + 35° t 8x + 28° u x =

Explanation:

Step1: Recall angle - sum property of a triangle

In a triangle inscribed in a semi - circle, the angle opposite the diameter is a right angle. So, in \(\triangle STU\), \(\angle T = 90^{\circ}\), and the sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 35^{\circ})+(8x + 28^{\circ})+90^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+8x+35^{\circ}+28^{\circ}+90^{\circ}=9x + 153^{\circ}\). So, the equation becomes \(9x+153^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(153^{\circ}\) from both sides: \(9x=180^{\circ}-153^{\circ}=27^{\circ}\). Then divide both sides by 9: \(x=\frac{27^{\circ}}{9}=3^{\circ}\).

Answer:

\(3\)