Question

are these triangles similar? yes no

Explanation:

Step1: Calculate the third angle of triangle \(HIJ\)

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle HIJ\), if two angles are \(39^{\circ}\) and \(111^{\circ}\), then the third angle \(\angle I=180^{\circ}-(39^{\circ} + 111^{\circ})=180^{\circ}-150^{\circ} = 30^{\circ}\)

Step2: Calculate the third angle of triangle \(UST\)

For \(\triangle UST\), if two angles are \(39^{\circ}\) and \(118^{\circ}\), then the third angle \(\angle U=180^{\circ}-(39^{\circ}+118^{\circ})=180^{\circ}-157^{\circ}=23^{\circ}\)

Step3: Check for angle - angle similarity

Similar triangles must have all three corresponding angles equal. Since the angles of \(\triangle HIJ\) (\(39^{\circ},111^{\circ},30^{\circ}\)) and \(\triangle UST\) (\(39^{\circ},118^{\circ},23^{\circ}\)) are not all equal.

Answer:

no