4. In \( \triangle A B C, \angle B \) measures exactly \( 101^{\circ} \) and \( \angle C \) measures less than \( 34^{\circ} \). Which of the following best describes the measure of \( \angle A \) ? F. Less than \( 45^{\circ} \) G. Greater than \( 45^{\circ} \) H. Equal to \( 34^{\circ} \) J. Equal to \( 45^{\circ} \) K. Equal to \( 135^{\circ} \)

To find the measure of \( \angle A \) in triangle \( ABC \), we can use the fact that the sum of the angles in a triangle is \( 180^{\circ} \). Given that \( \angle B = 101^{\circ} \) and \( \angle C < 34^{\circ} \), we can let \( \angle C = x \), where \( x < 34^{\circ} \). Now, we know that: \[ \angle A + \angle B + \angle C = 180^{\circ} \] Substituting the known values: \[ \angle A + 101^{\circ} + x = 180^{\circ} \] This simplifies to: \[ \angle A = 180^{\circ} - 101^{\circ} - x \] \[ \angle A = 79^{\circ} - x \] Since \( x < 34^{\circ} \), it follows that: \[ \angle A > 79^{\circ} - 34^{\circ} = 45^{\circ} \] Thus, \( \angle A \) must be greater than \( 45^{\circ} \). But wait, there's more! If you love math mysteries, this triangle problem is a great one for honing your angle deduction skills. By employing the logic of angle measures, you're actually practicing your problem-solving abilities—definitely a plus in both academic and real-world scenarios, like architecture or navigation! To dive deeper into the world of triangles, consider exploring some geometry books or engaging in online courses! From understanding the Pythagorean theorem to triangle congruence postulates, there's a whole treasure trove of knowledge waiting for you. Try well-reviewed resources on Khan Academy or even get a fun book like "The Joy of Geometry" for inspiration!