Questions: Given: Choices for 35-42 35. Find m angle C. 36. Find m angle E. 37. Are the corresponding angles congruent? 38. Find A C / D F. 39. Find C B / F E. 40. Find A B / D E. 41. Are the sides proportional? 42. Are the triangles similar? A) 1/4 B) 1/3 C) 1/2 D) 4/21 E) 41 degrees AB) 42 degrees (AC) 88 degrees AD) 89 degrees AE) Yes BC) No

Solution Steps

The sum of the angles in a triangle is $180^{\circ}$. In $\triangle ABC$, we have $m\angle A + m\angle B + m\angle C = 180^{\circ}$. Given $m\angle A = 50^{\circ}$ and $m\angle B = 42^{\circ}$, we have: $50^{\circ} + 42^{\circ} + m\angle C = 180^{\circ}$ $92^{\circ} + m\angle C = 180^{\circ}$ $m\angle C = 180^{\circ} - 92^{\circ}$ $m\angle C = 88^{\circ}$

The sum of the angles in a triangle is $180^{\circ}$. In $\triangle DEF$, we have $m\angle D + m\angle E + m\angle F = 180^{\circ}$. Given $m\angle D = 50^{\circ}$ and $m\angle F = 89^{\circ}$, we have: $50^{\circ} + m\angle E + 89^{\circ} = 180^{\circ}$ $139^{\circ} + m\angle E = 180^{\circ}$ $m\angle E = 180^{\circ} - 139^{\circ}$ $m\angle E = 41^{\circ}$

We have $m\angle A = 50^{\circ}$ and $m\angle D = 50^{\circ}$, so $\angle A \cong \angle D$. We have $m\angle B = 42^{\circ}$ and $m\angle E = 41^{\circ}$, so $\angle B \ncong \angle E$. We have $m\angle C = 88^{\circ}$ and $m\angle F = 89^{\circ}$, so $\angle C \ncong \angle F$. Since not all corresponding angles are congruent, the answer is No.

Final Answer