Question

what are the values of s and t? s = □° t = □°

Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are equal (marked with red ticks), it is an isosceles triangle. In an isosceles triangle, the base - angles (the angles opposite the equal sides) are equal. So \(s=t\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(s = t\). We know that one angle \(I=75^{\circ}\). Then \(s + t+75^{\circ}=180^{\circ}\). Substituting \(s = t\) into the equation, we get \(2s+75^{\circ}=180^{\circ}\).

Step3: Solve for \(s\) and \(t\)

First, subtract \(75^{\circ}\) from both sides of the equation \(2s+75^{\circ}=180^{\circ}\):
\(2s=180^{\circ}-75^{\circ}\)
\(2s = 105^{\circ}\)
Then divide both sides by 2: \(s=\frac{105^{\circ}}{2}=52.5^{\circ}\)

Since \(s = t\), \(t = 52.5^{\circ}\)

Answer:

\(s = 52.5\), \(t = 52.5\)