Question

c#13 in isosceles triangle rst, solve for x, and use it to find m∠str. x = m∠str =

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle \(RST\) (with \(RT = ST\)), \(\angle R=\angle S\). So \(2x + 14=32\).

Step2: Solve the equation for \(x\)

Subtract \(14\) from both sides of the equation \(2x+14 = 32\): \(2x=32 - 14\), \(2x=18\). Then divide both sides by \(2\): \(x = 9\).

Step3: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle STR=y\). We know \(\angle R = 32^{\circ}\), \(\angle S=32^{\circ}\). Then \(y+32 + 32=180\).

Step4: Solve for \(\angle STR\)

\(y=180-(32 + 32)\), \(y = 116^{\circ}\).

Answer:

\(x = 9\); \(m\angle STR=116^{\circ}\)