First, we need to figure out what exactly we can do to find the missing angles.
We can use the angle sum theorem to solve for the angles (and some other rules as well).
Angle 1:
We know we have two angles already there. 40 degrees and 90 degrees. Every triangle must have angles that add up to 180.
We can work this as so:
40 + 90 + angle 1 = 180
130 + a1 = 180
Subtract 130 from both sides...
130 - 130 + a1 = 180 - 130
a1 = 50
There! We now know that angle 1 is 50 degrees.
Next, angle two (this one is SUPER easy).
The angle directly above it is 90 degrees, so we can use the verticle angle rule to quickly see that angle 2 is 90 degrees as well. (Or we could just look at the paper and find out it's a right angle.)
Awesome! We know that angle 2 is 90. This will help us in finding angle 3 as well.
Let's use the angle sum theorem we used on angle 1.
a2 + a3 + 30 = 180
90 + a3 + 30 = 180
120 + a3 = 180
Subtract 120 from both sides...
120 - 120 + a3 = 180 - 120
a3 = 60
Sweet, we know can say angle three is 60 degrees!
Now, time for angle 4...
Angle three is right below angle 4... verticle angle rule comes into play here again:
a3 = a4
60 = a4
Angle 4 equals 60.
Now, time for angle 5. Let's use the angle sum rule for this one.
a4 + a5 + 60 = 180
60 + a5 + 60 = 180
120 + a5 = 180
Subtract...
120 - 120 + a5 = 180 - 120
a5 = 60
Angle 5 equals 60 degrees as well!
Almost there...hold tight.
Angle 6 is right below 5, so they equal each other because they are exactly verticle.
a6 = a5
60 = 60
Angle 7, sum theorem time!
a6 + a7 + 20 = 180
60 + a7 + 20 = 180
80 + a7 = 180
Subtract...
80 - 80 + a7 = 180 - 80
a7 = 100
Angle 7 equals 100!
Great, we're ... just saw the rest of the paper. Hold up.
To do part b, we need to find all the other angles to figure out angleX.
Look at the angle that is 45 degrees. Use verticle angle rule to see we have the triangle at 45 and 60 degrees.
60 + 45 + ? = 180
105 + ? = 180
? = 75 degrees.
Now we know the missing side is 75 degrees.
(I apologize, I can't exactly type it out how to do solve it, I do things differently than your school might teach. But I think the answer for B would be 243...but you might want to try it and see if that is correct.)
C.
This one, we need to use the sum rule we used above to find X.
First, add them all to equal 180:
4x + 28 + x + 19 + 3x + 13 = 180
Combine like terms.
8x + 60 = 180
Subtract...
8x + 60 - 60 = 180 - 60
8x = 120
Divide...
8x/8 = 120/8
x = 15
Fifteen equals X!
Now, D.
Since we know that they are equal (the lines going through the triangle's side shows us), we can set them equal and solve.
6k + 3 = 3k + 18
Simplify...
6k - 3k + 3 = 3k - 3k + 18
3k + 3 = 18
3k + 3 - 3 = 18 - 3
3k = 15
Divide 3 to get k by its self.
3k/3 = 15/3
k = 5
Now, we substitute k for 5 and solve.
6(5) + 3 =
30 + 3 = 33 (One side).
3(5) + 18 =
15 + 18 = 33
It is literally impossible to find the length of the other side without any given information about it. If there is, please let me know in the comments.
All righty! That was the longest thing I have ever attempted. (35 Minutes to answer this question.)
Hope I could help you out! If my math is wrong, or I provided an answer(s) you were not looking for, please let me know! However, if it my answer for you is EPIC, please consider marking Brainliest :) .
Have a good one;
God Bless.
