Answer:
<em>Assuming you want this rounded to the hundredths.</em>
6. x = 24.86
7. x = 4
8. x = 24.86
9. x = 12
10. x = 4
11. x = 20.57
Step-by-step explanation:
6. Because these angles are supplementary, they add up to 180 degrees. Using this, we can solve for x.
Step 1: Build your equation
3x + 5 + 4x + 1 = 180
Step 2: Combine like terms
7x + 6 = 180
Step 3: Subtract 6 from both sides of the equation.
7x = 174
Step 4: Divide the coefficient of x out.
x ≅ 24.68
7. Vertical Angles Theorem states that vertical angles are congruent. Now we can solve from there!
<em>(Note: There are two ways to solve this, but I picked the easier way)</em>
Step 1: Build your equation
3x + 5 = 4x + 1
Step 2: Collecting like terms on one side 1: Subtract 3x from both sides
5 = x + 1
Would you look at that! No coefficient on x. However, we need a sequel to fix the right side.
<em>(If you are wondering why there is no coefficient on x, the actual coefficient is 1. However, it is much cleaner to just ignore that.)</em>
Step 3: Collecting like terms on one side 2: Subtract 1 from both sides.
4 = x
Because equations don't care about silly human things like which terms are on which side, you can also arrange it like this:
x = 4
8. A linear pair of angles are adjacent angles formed by two intersecting lines. The measure of a linear pair of angles is 180 degrees. See #6 for details on how to solve this.
9. Complementary angles add up to 90 degrees. Similar to supplementary angles, this can be solved but setting the sum to 90 degrees.
Step 1: Build your equation.
3x + 5 + 4x + 1 = 90
Step 2: Combine like terms.
7x + 6 = 90
Step 3: Subtract 6 from both sides of the equation.
7x = 84
Step 4: Divide the coefficient of x from both sides.
x = 12
10. Because they are congruent, you can set the angles equal to eachother. Please view #7 for how to solve this.
11. Similiar to #6 and #9, we can set the sum to 150 degrees and solve from there.
Step 1: Build your equation.
3x + 5 + 4x + 1 = 150
Step 2: Combine like terms.
7x + 6 = 150
Step 3: Subtract 6 from both sides of the equation.
7x = 144
Step 4: Divide the coefficient of x from both sides.
x ≅ 20.57
There you have it! Wow, I haven't done algebra like that since 2019!
Hope I helped!
