What Is an Angle?

Mathematics · Geometry · ages 9-10

Name ______________________ Date ____________

Zadie draws two straight rays that start from the exact same dot and point in different directions, not opposite ones. What has she drawn?
- A straight line, because the rays are straight
- An angle, because two straight rays share one starting point
- A circle, because the rays point in different directions
Look at any corner of a flat polygon. What meets at that corner?
- One side all by itself
- Two sides of the shape
- Three sides at once
Which classroom object shows an angle?
- An open door seen from above, with hinge and open/closed directions
- A flat wall with no corners, no hinge, and no meeting point
- A straight ruler edge with no bend and no vertex
- A round ball with no corner and no shared point
An angle is made from rays that share one vertex. How many rays meet to form one angle?
Answer: ______________
Two rays share a vertex. One is drawn very short and one very long. A student says the short ray cannot be an arm of an angle. Is the student right?
Circle one: True False
How many vertices does a square have?
- 3
- 4
- 5
A triangle is shown. How many vertices (corners) does it have?
Answer: ______________
A rectangle has 4 corners, so it has 4 angles.
Circle one: True False
Sara wants the clock hands to show an obtuse angle, using the smaller opening between the hands. The minute hand points at 12. Where should she point the hour hand?
- At 3, to make a square corner
- At 4, to make an angle wider than a right angle and less than a half turn
- At 1, to make an angle smaller than a right angle
A pentagon has 5 vertices and a triangle has 3 vertices. How many more vertices does the pentagon have?
- 1 more
- 2 more
- 8 more

Answer key

For grown-ups. Fold this page away before handing over the rest.

What Is an Angle? W1-mt_3S10OOGPqu-s1

An angle, because two straight rays share one starting point · Two straight rays that start from the same point and point in nonopposite directions make an angle.
Two sides of the shape · At every corner of a flat polygon, two sides meet, like the two arms of an angle.
An open door seen from above, with hinge and open/closed directions · An open door seen from above shows the hinge point and the open and closed directions, giving two ray directions from one shared point.
2 · One angle needs 2 rays sharing one vertex.
False · Arm length does not set the opening. Two rays sharing a vertex form an angle whatever their drawn lengths, because the angle is the opening between the directions.
4 · A square has 4 corners, and each corner is a vertex where two sides meet.
3 · Each corner of the triangle is a vertex, where two sides meet like the arms of an angle.
True · Every corner of a shape is a vertex holding one angle, so 4 corners means 4 angles.
At 4, to make an angle wider than a right angle and less than a half turn · Obtuse means greater than a right angle and less than a half turn. Pointing at 4 goes past the square corner at 3, so the smaller opening is obtuse.
2 more · Pair up 3 corners of the pentagon with the 3 corners of the triangle. 2 corners are left over, so the pentagon has 2 more vertices.