Triangle ABC is an isosceles right triangle. What is the measure of one base angle? \( 30^{\circ} \) \( 45^{\circ} \) \( 60^{\circ} \) \( 90^{\circ} \)

In an isosceles right triangle, the two base angles are equal, and the sum of all angles in any triangle is \( 180^{\circ} \). Therefore, if we let each of the base angles be \( x \), we can express this as: \( x + x + 90^{\circ} = 180^{\circ} \). Solving for \( x \) gives us \( x = 45^{\circ} \). So, the measure of each base angle in triangle ABC is \( 45^{\circ} \). Triangles like this are foundational in trigonometry and geometry. The \( 45-45-90 \) triangle has special properties; the lengths of the legs are equal, and the hypotenuse can be found using the formula \( h = l\sqrt{2} \), where \( l \) is the length of a leg. This is a useful relationship when solving real-world problems involving slopes or diagonal cuts!