Question

are these triangles similar? yes no

Explanation:

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

The sum of angles in a triangle is \( 180^{\circ} \). For \( \triangle UVW \), let the third angle be \( \angle U \). Then \( \angle U=180^{\circ}-(85^{\circ} + 38^{\circ})=180^{\circ}-123^{\circ} = 57^{\circ} \)

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

For \( \triangle QRS \), let the third angle be \( \angle S \). Then \( \angle S=180^{\circ}-(85^{\circ}+31^{\circ})=180^{\circ}-116^{\circ}=64^{\circ} \)

Step3: Check for angle - angle similarity

Two triangles are similar if their corresponding angles are equal. The angles of \( \triangle UVW \) are \( 85^{\circ},38^{\circ},57^{\circ} \) and the angles of \( \triangle QRS \) are \( 85^{\circ},31^{\circ},64^{\circ} \). Since not all corresponding angles are equal.

Answer:

no