Answers:
- Problem 1) 40 degrees
- Problem 2) 84 degrees
- Problem 3) 110 degrees
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Explanation:
For these questions, we'll use the inscribed angle theorem. This says that the inscribed angle is half the measure of the arc it cuts off. An inscribed angle is one where the vertex of the angle lies on the circle, as problem 1 indicates.
For problem 1, the arc measure is 80 degrees, so half that is 40. This is the measure of the unknown inscribed angle.
Problem 2 will have us work in reverse to double the inscribed angle 42 to get 84.
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For problem 3, we need to determine angle DEP. But first, we'll need Thales Theorem which is a special case of the inscribed angle theorem. This theorem states that if you have a semicircle, then any inscribed angle will always be 90 degrees. This is a handy way to form 90 degree angles if all you have is a compass and straightedge.
This all means that angle DEF is a right angle and 90 degrees.
So,
(angle DEP) + (angle PEF) = angle DEF
(angle DEP) + (35) = 90
angle DEP = 90 - 35
angle DEP = 55
The inscribed angle DEP cuts off the arc we want to find. Using the inscribed angle theorem, we double 55 to get 110 which is the measure of minor arc FD.
Answer:
27.9 i think in in a fraction 12 / 43
Step-by-step explanation:
Answer:
Hi there! Sorry if my comment doesn't help you! I'm only here for the points! Thank you anyway!
Step-by-step explanation:
Answer:
See below.
Step-by-step explanation:
13. D
Simply subtract. 85376 - 37793 = 47583.
14. C
[Something] - 32497 = 26348
Add 32497 to both sides:
[Something] - 32497 + 32497 = 26438 + 32497
[Something] = 58845
15. C
Compute each difference:
A: 51455 - 26478 = 24977
B: 49351 - 15274 = 34077
C: 63286 - 37439 = 25847
(D: 46307 - 21550 = 24757)
16. B
Simply subtract:
143864 - 112955 = 30909
17. A
First, find the difference:
85732 - 39864 = 45868
Only 45798 (A) is less than 45868.
(Note that B is equal to, not less than).
18. C
Subtract:
45932 - 29574 = 16358.
19. B
Subtract:
96834 - 31727 = 65107 - 12156 = 52951
20. C
27301 - 12352 - [Something] = 7356
14949 - [Something] = 7356
Add [Something] to each side:
14949 = 7356 + [Something]
Subtract 7356 from each side.
7593 = [Something]
Note: Do you need help with subtraction specifically? These questions can be solved with simply with a calculator, but perhaps that is not the intention here. Anyways, I recommend using Khan Academy to improve your arithmetic skills if necesary.
