Download Geometry Worksheet 3

Geometry Worksheet 3
Name: _________________________
Venn Diagrams: 1. Out of 28 students, 12 have at least one brother and 13 have at least one sister. Eight students
have both brothers and sisters.
a. Make a Venn Diagram:
b. How many students do not have either a brother or a sister?
2. In a class of 64 band students at a high school, 30 students liked country music, 20 students liked rap, and 28 students liked Pop music. 8 students say they listen to country and rap music, and of those 3 listen to pop as well. 4 only listen to country and 7 only listen to Pop. a. Make a Venn Diagram: b. How many students don’t listen to country, rap or pop music? 3. In a college class of 125 students, 65 said they are taking the basic math class and 85 said they were taking the basic English class. 25 said that they were not taking either one. a. Draw a Venn Diagram: c. How many students are taking both basic math and English? Give an algebraic equation for each and then solve.
4. The measure of the angles of a triangle are given as 4x, (6x+5), and (5x-20). What are the
measures of each angle? Write an equation and show the work.
5. In a certain triangle, the measure of one angle is 4 times the measure of the smallest angle, and
the measure of the remaining angle is twice the sum of the measures of the other two angles.
Determine the measure of each angle. Write an equation and show the work.
6. The second angle of triangle is 35 degrees less than 7 times the first angle. The third angle is 20
degrees more than twice the first. Find the measures of the three angles. Write an equation and
show the work.
7. Determine the measure of each interior angle in a regular heptagon (7 sided figure). Prove your answer – show work.