Question

10 choose the options that best fit the blank boxes. (1 point) given m || n, m∠1 = 50°, m∠2 = 40°, and line s bisects ∠adc. prove m∠3 = 40°. it is given that m || n, m∠1 = 50°, m∠2 = 40°, and line s bisects ∠adc. by the blank 1, m∠def = 90°. because blank 2, angles formed by two parallel lines and a transversal are blank 2. ∠def ≅ ∠abc, so m∠abc = 90°. by the blank 3, angles blank 3. consequent, and m∠4 is half m∠abc. so m∠4 = 40°. because vertical angles are congruent, ∠3 ≅ ∠4. finally, m∠3 = m∠4 by the angle - congruence postulate, so m∠3 = 40° by the blank 4. definition of a bisector substitution property of equality alternate exterior angle addition postulate

Explanation:

1. For the first blank related to why \(m\angle DEF = 98^{\circ}\), it could be due to the angle - addition postulate if \(\angle DEF\) is composed of two adjacent angles whose measures sum up to \(98^{\circ}\).
2. For the second blank, since we are talking about angles formed by parallel lines and a transversal, the term 'alternate exterior' could be relevant if the angles in question are in an alternate - exterior relationship.
3. For the third blank, when we say \(\angle DEF\cong\angle ABC\) and then use the measure of \(\angle DEF\) to find the measure of \(\angle ABC\), we are using the substitution property of equality.
4. For the fourth blank, when we use the fact that a line bisects \(\angle ADC\) to find the measure of \(\angle 4\) and then equate \(\angle 3\) and \(\angle 4\) (because of vertical - angle congruence) and finally find \(m\angle 3\), we are using the definition of a bisector.

Answer:

1. angle addition postulate
2. alternate exterior
3. substitution property of equality
4. definition of a bisector