Problem 44
The term "bisect" means "cut in half".
Since BD bisects angle ABC, this means the smaller angles ABD and DBC are congruent.
angle ABD = angle DBC
x+15 = 4x-45
15+45 = 4x-x
60 = 3x
3x = 60
x = 60/3
x = 20
<h3>Answer: x = 20</h3>
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Problem 45
We use the same idea as the previous problem
angle ABD = angle DBC
2x+35 = 5x-22
35+22 = 5x-2x
57 = 3x
3x = 57
x = 57/3
x = 19
<h3>Answer: x = 19</h3>
If triangles AMN and ABC are similar, then
AM/AB = AN/AC
or
AM/(AM + MB) = AN/(AN + NC)
Check if this is true:
AM/AB = 21/(21 + 9) = 21/30 = 7/10
AN/AC = 14/(14 + 6) = 14/20 = 7/10
The angle at vertex A is common to both of the triangles.
Then by the side-angle-side (SAS) similarity theorem, the triangles are indeed similar.
We can convert 7/10 to a decimal first.
7/10 = 0.7
Now we can multiply this problem easier.
35 x 0.7 = 24.5
Olivia applied the scale factor to the measurements of the model she saw. We need to know those in order to calculate the new ones.
Answer:
The circumference of the circle is <u>C-72.22 </u><u>units</u>
Step by step explanation-
Given-
- Diameter of circle (d) = 23 units
- π = 3.14
Now,
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