Question

what is the value of x? x + 20° x =

Explanation:

Step1: Recall isosceles - triangle property

Since $RT = RS$ (marked by the red - hash marks), $\triangle RTS$ is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, $\angle T=\angle S=x + 20^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle RTS$, we have $\angle T+\angle S+\angle R=180^{\circ}$. Since $\angle T=\angle S=x + 20^{\circ}$, and let $\angle R = y$ (but we don't need to find $y$ explicitly). So, $(x + 20)+(x + 20)+y=180$. Also, since $TS$ is a diameter, $\angle R = 90^{\circ}$ (angle inscribed in a semi - circle). Then the equation becomes $(x + 20)+(x + 20)+90=180$.

Step3: Simplify the equation

Combine like terms: $2x+20 + 20+90=180$, which simplifies to $2x+130 = 180$.

Step4: Solve for $x$

Subtract 130 from both sides of the equation: $2x=180 - 130=50$. Then divide both sides by 2: $x=\frac{50}{2}=25$.

Answer:

$25$