Answer:
Step-by-step explanation:
<u>QUESTION 7:</u>
We are trying to find angles 1 and 2.
Known angle: 107˚.
In this question, we have 2 parallel lines with a <u>transversal</u>. A transversal is a line that passes through 2 parallel lines making it so that the angles on both sides are exactly the same.
Step 1: Find the measures of all the angles using the one we already know.
I will start with the angle adjacent (right next to) the angle that measures 107˚. As you can see, it is a supplementary angle because both of them form a straight line, or 180˚.
Therefore,
107+x= 180
x= 180-107
x= 73˚
Next, I will find the measure of the angle that is vertical to the one that measures 107˚. Note that angles that are vertical to each other are always identical, or in other words they have the same measure. Hence, the angle "vertical", or opposite to the one that measures 107˚ has to measure 107˚ as well. You can also tell this is true because they look the same.
Now I'll find the measure of the angle vertical to the one that measures 73˚. As we know, vertical angles are identical, so the one vertical to it is 73˚.
Here, I'll solve for angles 1 and 2. Like I said earlier, when a transversal crosses through 2 parallel lines, there will be 2 sets of angles that all have the same measurements.
To solve for angle 1, simply know what angle is right below it, and that is the one that measures 107˚. (If you look at the 2 lines, you will see that both angle sets are essentially duplicates of each other.) Likewise, angle 2 has to be 73˚ because the one under it is also 73˚.
Angle 1: 107˚
Angle 2: 73˚
<u>QUESTION 8:</u>
Again, we have a transversal that passes through 2 parallel lines. One angle measures 95˚. When there are 3 seperate angles along a straight line, the one next to the one with the given measurement will be the same as that one.
So angle 3 is 95˚. To find angle 4, find the angle measurement that's vertical to angle 3, which is 95˚. Now, since that angle and angle 4 are supplementary (both form a straight line which is always 180˚), 95+x= 180.
(x stands for angle 4)
x+95= 180
x= 180-95
x= 85
Angle 4= 85˚.
<u>QUESTION 9: </u>
ANGLE 5: 49˚
When there is a transversal, there are 2 identical pairs of angles. Therefore, angle 5 must be 49˚.
ANGLE 6: 131˚
angle 5 and angle 6 form a straight line which means they are supplementary angles. Therefore, both angles must add up to 180˚. So 49+x= 180
x= 180-49= 131
(x stands for angle 6)
Hope this helps!! Also I worked pretty hard on this so brainliest would be appreciated :D
Practice problems if it helps :) : https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_1
