Question

4 ( m angle 1 + m angle 2 + m angle 3 = 180 ^ { circ } ) substitution (2,3)
what was the first mistake in joes proof?
choose 1 answer:

a constructing a parallel line like this isnt necessarily
possible.

b angles ( angle 4 ) and ( angle 2 ) are not alternate interior angles, and
neither are ( angle 1 ) and ( angle 5 ).

c angles ( angle 3 , angle 4 ), and ( angle 5 ) dont form a straight angle.

d the substitution isnt correct.

Explanation:

To prove the sum of angles in a triangle is \(180^{\circ}\), one common method is to construct a parallel line. If the parallel line is constructed, then \(\angle1\) and \(\angle5\) are alternate - interior angles (if the parallel line is drawn correctly), and \(\angle2\) and \(\angle4\) are alternate - interior angles. Alternate - interior angles are equal when a transversal intersects two parallel lines. Then, since \(\angle3+\angle4+\angle5 = 180^{\circ}\) (they form a straight line), by substitution \(m\angle1 + m\angle2+m\angle3=180^{\circ}\). But if the construction of the parallel line is wrong (for example, if the line is not actually parallel), then the relationships of alternate - interior angles (\(\angle1\) with \(\angle5\) and \(\angle2\) with \(\angle4\)) do not hold.

Answer:

B. Angles \(\angle4\) and \(\angle2\) are not alternate interior angles, and neither are \(\angle1\) and \(\angle5\).