Angle Sums of Polygons
What does it mean when it asks you to find the sum of the interior angles of a polygon.
To find the total angle measure for the shape
Whenever we don't know the measurement of an angle, what can we write in its place
A variable
What is the difference between the terms congruent and similar?
Congruent means that the two figures are exactly the same size and shape.
Similar means the two figures have the same shape but different size.
If I need to triple a recipe, how much of each ingredient would I need?
1 tsp of vanilla
2 tbsp of sugar
1.5 cups of flour
3 tsp of vanilla
6 tbsp of sugar
4.5 cups of flour
Angles that form a straight line are called....
Supplementary angles
What equation can we use to find the sum of interior angles of any polygon?
S = (n-2)x180
A triangle has angle measurements: 111 and and 39. Find the missing angle.
30 degrees
Triangles are similar if their angle measures are....
the same or equal
A 5ft tall person casts a shadow that is 3 ft long. They are standing near a flagpole that casts a shadow that is 36ft long. How tall is the flagpole.
60 feet tall
How do you find the measurement of an exterior angle of a triangle?
Add the two inside angles
What is the sum of the interior angles of a hexagon?
720 degrees
A quadrilateral has angles measurements of: 56, 90, 90 degrees. Find the missing angle measurement.
124 degrees
Triangle A: 90 degrees, 42 degrees, x
Triangle B: 90 degrees, 58 degrees, y
Prove whether the triangles are similar
x = 48 degrees and y =32 degrees
No the triangles are not similar because not all of their angles are the same
Triangle A has a height of 300 feet and a base of 240 feet
Triangle B has a height of x feet and a base of 7.5 feet
What is the height of Triangle B?
9.375 feet
Name a angle relationship where the two angles measurements are equal to each other:
Possible answers are:
Vertical, Corresponding, Alt. Interior, Alt. Exterior
A stop sign is in the shape of a regular octagon. What is the measure of each interior angle?
135 degrees.
A heptagon (7 sides) has angles measurements: 84, 167, 104, 126, 140, 159. Find the missing angle measurement.
120 degrees
Define corresponding angles
Angles that are in matching locations in two different shapes
or Angles that if shifted over would be the same spot
What does it mean for sides to be proportional
You can determine the side lengths by either using multiplication or division
The ratio of the interior angles of a triangle are 2:4:9. find the measures of each angle.
24 degrees, 48 degrees, 108 degrees
The interior angles of a regular polygon each measure 144 degrees. How many sides does the polygon have?
10 sides
130 degrees
What symbol do we use to show if two shapes are similar? (We learned this way back in Chap. 2)
~
Define indirect measurement:
Measuring something else in order to measure something that is too difficult or impossible to measure by hand.
For a shape to be considered a polygon, it must follow three rules which are...
1. No openings (closed)
2. No curved sides
3. Sides can only connect at the endpoints