On a coordinate grid, the coordinates of vertices p and q for polygon pqrs are p(1, 2) and q(−1, 2). what is the length of side pq of the polygon?
2 units
3 units
4 units
6 units

2 units

Polygons are shapes with straight sides and must be closed. Also, polygons sides never touch. Polygons are classified according to its number of sides. Since in this problem we have four points because the polygon is PQRS, then this is a Quadrilateral, which is any polygon with exactly 4 sides. We only know two points P(1, 2) and Q(−1, 2). To find the length of Side PQ of the polygon we must use the distance formula:

Finally, the length of Side PQ of the polygon is 2 units

m∠7 = 63 degrees

m∠8 = 117 degrees

m∠9 = 63 degrees

Step-by-step explanation:

When two lines intersect at a point, then they formed 2 pairs of vertically opposite angles and 4 pairs of linear angles

In the given figure

∵ There are two lines intersected at a point

∴ The angle of measure 117° and ∠8 are vertically opposite angles

∴ ∠7 and ∠9 are vertically opposite angles

∴ The angle of measure 117° and ∠7 are linear angles

∵ The vertically opposite angles are equal in measures

∴ The angle of measure 117° and ∠8 are equal in measures

∴ m∠8 = 117°

∵ The sum of the measures of the linear angles is 180°

∴ m∠7 + 117° = 180°

→ Subtract 118 from both sides

∵ m∠7 + 117 - 117 = 180 - 117

∴ m∠7 = 63°

∵ m∠7 = m∠9 ⇒ proved up

∴ m∠9 = 63°