5.) We know that all of the angles in a triangle add up to 180 degrees. To solve:
m∠w = 80°
6.) x° and 70° should equal 180°. Let's set up an equation:
m∠x=110°
7.) We know that due to the vertical angles theorem, 60° will be congruent to 60° where they intersect. Since we now know two angles inside the bottom triangle, we can set up an equation to solve for k.
m∠k = 60°
8.) Finally, we know that angles next to each other when they are perpendicular = 180°. Since we know that proof, we can set up an equation to solve for p.
1) the sum of all three angles in a triangle is always 180, so number 5 is w=80
2)I assume they mean x. since the x angle and the 70 angle are a linear pair they must add to 180, so x has to be 110
3) the top 60 angle makes a vertical angles with the angle right below it. since vertical angles are congruent, the angle below has to be 60 also. again all 3 must add to 180 so o is also 60
4) these are all linear pairs. every angle shown has to be 90
320 students. Because you have to divide 384 by 6 which will give you 64 which is the number for the students that chose art and then subtract that from the total students which are 384 and you'll get 320 as your answer for the student that didn't pick art.
