Question

It is given that line AB is parallel to CD, and points E, G, H, and F are collinear. The measure of angle EGF is 180°. By the definition of a straight angle, angle AGE and angle AGF are adjacent, so the measure of angle AGE plus the measure of angle AGF equals the measure of angle EGF, by the Angle Addition Postulate. Then, substituting for the measure of angle EGF it can be said that the measure of angle AGE plus the measure of angle AGF equals 180°. ______, so the measure of angle CHE plus the measure of angle AGF equals 180°. Substituting once again means that the measure of angle AGE plus themeasure of angle AGF equals the measure of angle CHE plus the measure of angle AGF. The measure of angle AGE is equal to the measure of angle CHE ______. Finally, by the definition of congruence, angle AGE is congruent to angle CHE.

A) Angles CHE and angle AGF are alternate interior angles; using the Addition Property of Equality.
B) Angle CHE and angle AGF are alternate interior angles; using the Subtraction Property of Equality.
C) Angle CHE and angle AGF are same-size interior angles; using theSubtraction Property of Equality.
D) Angle CHE and angle AGF are same-side interior angles; using the Addition Property of Equality.

Answer 1

By the Angle Addition Postulate, the measure of angle AGE plus the measure of angle AGF equals the measure of angle EGF. Therefore, the measure of angle AGE plus the measure of angle AGF equals 180°. The correct option is A) Angles CHE and angle AGF are alternate interior angles; using the Addition Property of Equality.

Step-by-step explanation:

From the given information, we know that angle EGF is 180° and angle AGE and angle AGF are adjacent. By the Angle Addition Postulate, the measure of angle AGE plus the measure of angle AGF equals the measure of angle EGF, which is 180°. Therefore, the measure of angle AGE plus the measure of angle AGF equals 180°.

This implies that the measure of angle CHE plus the measure of angle AGF equals 180°. Additionally, since angle AGE is congruent to angle CHE, the measure of angle AGE is equal to the measure of angle CHE. Therefore, the correct option is A) Angles CHE and angle AGF are alternate interior angles; using the Addition Property of Equality.