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
