Name __ANSWERS______
REVIEW for Shapes and Designs Unit Test
1.What is the interior angle sum of a regular hexagon? Show your work.
Sum = 180 x 6 – 360 = 720
2. How many degrees are in one exterior angle of a regular hexagon?
First, find the measure of each interior angle. (180 x 6 – 360) 6 = 120
Then, subtract the interior angle from 180 to get the exterior angle:
180-120 = 60 OR divide 360 by 6 = 60
- What is the interior angle sum of a regular decagon? Show your work?
Sum = 180 x 10 – 360 = 1440
4. How many degrees are in one exterior angle of a regular decagon?
First, find the measure of each interior angle. (180 x 10 – 360) 10 = 144
Then, subtract the interior angle from 180 to get the exterior angle:
180-144 = 36 OR divide 360 by 10 = 36
5. A triangle has sides of 6 and 7 units. The longest side is missing. What are possible measurements for the longest side?
The longest side must be less 13 units and greater than 7 units
6. Is a triangle with angle measures 52°, 30°, and 100° possible? Explain why
or why not.
NO- 52 + 30 + 100 = 182, the three angles of a triangle must equal 180
7. Is a triangle with angle measures 40°, 50°, and 90° possible? Explain why
or why not.
YES- 40 + 50 + 90 = 180 and the three interior angles of a triangle must be equal to 180
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Review (continued)
8. Estimate the measures of the angles below.
a.about 50 / b.
About 120
9. Use rectangle ABCD with diagonal DB. Find the measure of the angle
marked x. Show your work.
The angle at vertex C must be 90 since it is a rectangle.
X + 90 + 61 = 180, so x = 29
Shapes and Designs
REVIEW (continued)
10. Use the figure below which shows parallel lines and a transversal.
The measure of 2 is 46°. Find the measures of angles 1, 3, and 6.
Explain how you found each measure.
a. measure of 1 = 134 b/c angles 1 and 2 are supplementary (=180)
b. measure of 3 = 46 b/c it is a vertical angle to angle 2
c. measure of 6 = 46 b/c angles 2 and 6 are corresponding so they must be congruent
11. Suppose the measure of an angle is 52°. What is the measure of its
complementary angle?
Complementary add to 90, so 90 – 52 = 38
Draw the angles to show that you are correct.
12. Suppose two angles are supplementary and one of them measures 49°.
What is the measure of the other angle?
Supplementary add to 180, so 180 – 49 = 131
Draw the angles to show that you are correct.
REVIEW continued
13. Draw a parallelogram with two sides of length 15 cm, two sides of length
8 cm, and angles of 60° and 120°.
14. Is it possible to build a quadrilateral with the given side lengths? Why or why not?
a. 5, 6, 8, 9
YES because 5 + 6 + 8 = 19 which is more than 9 (the longest side)
b. 5, 3, 2, 12
No because 5 + 3 + 2 = 10 which is less than 12 (the longest side)