If one base angle of an isosceles triangle is \( 35^{\circ} \). What is the vertex angle? \( 55^{\circ} \) \( 35^{\circ} \) \( 110^{\circ} \) \( 60^{\circ} \)

In an isosceles triangle, the two base angles are equal. If one base angle is \( 35^{\circ} \), then the other base angle is also \( 35^{\circ} \). To find the vertex angle, you can use the fact that the sum of the interior angles in a triangle is \( 180^{\circ} \). So, you can calculate the vertex angle as follows: Vertex angle = \( 180^{\circ} - (35^{\circ} + 35^{\circ}) = 180^{\circ} - 70^{\circ} = 110^{\circ} \). Thus, the vertex angle is \( 110^{\circ} \). If you ever find yourself caught in a triangle riddle, remember this fun fact: an isosceles triangle gives off vibes of symmetry! Since the two base angles are equal, your work can often be simplified by knowing just one of them. Keeping that in mind can save time during geometry quizzes! For further exploration, dive into the world of triangle types! Beyond isosceles, there are equilateral triangles where all angles are \( 60^{\circ} \), and scalene triangles with all sides of different lengths, leading to unique angle measures. Exploring their properties and the Pythagorean theorem can deepen your understanding of the fascinating world of geometry!