Question

enter the answer in each space provided. use numbers instead of words. since lines a and b are parallel and t is a transversal, angles 2 and 4 are congruent by the corresponding angles theorem. the measure of angle 2 equals the measure of angle 4 by definition of congruent angles. angles 1 and \boxed{} are supplementary because they form a linear pair. so, m∠1 + m∠\boxed{} = 180° by the definition of supplementary angles. by substitution, m∠1 + m∠4 = 180°. so, ∠1 and ∠\boxed{} are supplementary angles by definition of supplementary angles.

Explanation:

Step1: Analyze Angles 1 and its Supplementary Angle

Angles forming a linear pair are supplementary. Angle 1 and angle 2 form a linear pair (assuming standard transversal - parallel lines diagram where angle 1 and angle 2 are adjacent and form a straight line). So angles 1 and 2 are supplementary.
<Reasoning: Linear pair implies supplementary angles>

Step2: Analyze the Substitution and Final Supplementary Angle

We know \( m\angle1 + m\angle2=180^\circ \) and \( m\angle2 = m\angle4 \) (from congruent angles). By substitution, \( m\angle1 + m\angle4 = 180^\circ \), so \( \angle1 \) and \( \angle4 \) are supplementary.
<Reasoning: Substitute \( m\angle2 \) with \( m\angle4 \) in the supplementary angle equation>

Answer:

For the first blank (angles 1 and \(\square\) supplementary): 2
For the second blank (\(m\angle1 + m\angle\square= 180^\circ\)): 2
For the third blank (\(\angle1\) and \(\angle\square\) supplementary): 4

(Assuming the standard diagram where angle 2 and angle 4 are corresponding angles, angle 1 and angle 2 are linear pair, and using substitution with angle 4)