Question

1. Construct a line parallel to line segment AB through point P. For the first step in your construction, you must use the given point Q to draw a line connecting point P to segment AB. Extend your segment beyond both points.
2. Given m<PQB =52 , solve for all angles formed by the parallel lines (segment AB and your newly constructed parallel line) cut by the transversal (the segment containing points P and Q).
3. Identify all pairs of angles (alternate interior, alternate exterior, corresponding, and consecutive interior) by labeling each angle you solved in step 2 with a letter or symbol.

Answer 1

Answer on Question #44206, Math, Geometry

1. Construct a line parallel to line segment AB through point P. For the first step in your construction, you must use the given point Q to draw a line connecting point P to segment AB. Extend your segment beyond both points.

2. Given $m < PQB = 52$ , solve for all angles formed by the parallel lines (segment AB and your newly constructed parallel line) cut by the transversal (the segment containing points $P$ and $Q$ ).

3. Identify all pairs of angles (alternate interior, alternate exterior, corresponding, and consecutive interior) by labeling each angle you solved in step 2 with a letter or symbol.

Answer.

Alternate interior angles: $\angle 1$ and $\angle 7$ , $\angle 2$ and $\angle 8$ .

Alternate interior angles: $\angle 3$ and $\angle 5$ , $\angle 4$ and $\angle 6$ .

Corresponding angles: $\angle 1$ and $\angle 5$, $\angle 2$ and $\angle 6$, $\angle 3$ and $\angle 7$, $\angle 4$ and $\angle 8$.

Consecutive interior angles: $\angle 1$ and $\angle 8$, $\angle 2$ and $\angle 7$.

Vertical angles: $\angle 1$ and $\angle 3$, $\angle 2$ and $\angle 4$, $\angle 5$ and $\angle 7$, $\angle 6$ and $\angle 8$.

If $m\angle 2 = 52{}^{\circ}$, then $m\angle 4 = 52{}^{\circ}$, $m\angle 6 = 52{}^{\circ}$, $m\angle 8 = 52{}^{\circ}$,

$$m \angle 1 = 128{}^{\circ}, \quad m \angle 3 = 128{}^{\circ}, \quad m \angle 5 = 128{}^{\circ}, \quad m \angle 7 = 128{}^{\circ},$$

www.AssignmentExpert.com