Name: ____________
Practice Quiz
Investigation 2: Designing Polygons: the angle connection
1. Is it possible for a triangle to have a 65° angle and a 115° angle? Explain why or why not?
2. The polygon below is a regular octagon. Find the value of x.
x
3. Use the following pentagon.
Find the measures of angles 1, 2, x, and y.
Measure of angle 1________
2
Measure of angle 2_________
Measure of angle x_________
1
Measure of angle y_________
Explain how you know the measures in part (a) are correct without using an angle ruler or
protractor.
4. What is the angle sum of a 12-sided polygon? Show your work.
Name: ___KEY_________
Practice Quiz
Investigation 2: Designing Polygons: the angle connection
5. Is it possible for a triangle to have a 65° angle and a 115° angle? Explain why or why not?
No, when you add the two angles up, it makes 180. A triangle has 180 degrees, but you only
used 2 angles. There is no room for another angle.
Remember if you have 2 angles, they should add to be LESS than 180, so there is room for the
last angle.
6. The polygon below is a regular octagon. Find the value of x.
x
First you need to find how many degrees are in n octagon, use
the formula (s-2)*180. And you find that there are 1080 degrees
in the whole thing. Now find the degrees in one angel: 1080
divided by 8 = 135 for each angle. Now look at just the triangle.
You know the obtuse angle (135 degrees), subtract from 180 and
split in half. This is your missing angle. X=22.5
7. Use the following pentagon.
Find the measures of angles 1, 2, x, and y.
This is a lot of supplementary angle measures.
Measure of angle 1___113
(180-67)
Measure of angle 2__105
(180 – 75)
Measure of angle x__90
the box is 90 so 180-90
2
1
Measure of angle y___64 after you find the others
You need to know a pentagon is 540 degrees, so subtract all the inside angles. The arc means
congruency, so remember to divide by 2. Then you can subtract to find y (180 – 116)
Explain how you know the measures in part (a) are correct without using an angle ruler or
protractor.
You need to know how to use supplementary angles and how to find the inside degrees of a
polygon. The pentagon has 540 degrees.
8. What is the angle sum of a 12-sided polygon? Show your work.
Use the formula: (s-2 ) 180
(12-2) 180
1800