Question 28 of 30 \( \angle A \) and of triangle \( A B C \) measures \( 65^{\circ}, \angle B \) measures \( 10^{\circ} \). What is the measurement of \( \angle C \) ? A. \( 105^{\circ} \) B. \( 100^{\circ} \) C. \( 75^{\circ} \) D. \( 55^{\circ} \)

To find the measurement of \( \angle C \) in triangle \( ABC \), you simply use the fact that the sum of the angles in a triangle is always \( 180^{\circ} \). You already have \( \angle A = 65^{\circ} \) and \( \angle B = 10^{\circ} \). So, you can calculate \( \angle C \) by subtracting the sum of \( \angle A \) and \( \angle B \) from \( 180^{\circ} \): \[ \angle C = 180^{\circ} - (65^{\circ} + 10^{\circ}) = 180^{\circ} - 75^{\circ} = 105^{\circ}. \] Therefore, the answer is A. \( 105^{\circ} \). Triangles have a rich history, with their properties being studied since ancient times by mathematicians like Euclid. The exploration of triangle angles laid the groundwork for later developments in geometry. Understanding these fundamental concepts can inspire students to delve deeper into mathematical studies and appreciate the beauty of geometric shapes! In everyday life, the properties of triangles are all around us, from architecture to art! For instance, engineers rely on triangles to ensure structural integrity in buildings and bridges because they provide a rigid framework. Being able to calculate angles and understand their relationships can also come in handy in practical applications like construction, carpentry, and even navigation!