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:
An inequality that represents this word sentence is >. The solution is. x > 17.
Step-by-step explanation:
You need to calculate 35% of 400.
The way I do this on paper is I split it up into chunks and then add the chunks together.
First I would calculate 10%. To do this, divide 400 by 10, because to get from 100% to 10% you must divide by 10.
So 10% = 40
You need 30%, so you just multiply by 3, because to get from 10% to 30%, you multiply by 3.
So 30% = 120
5% is half of 10% so half of 40 is 20.
So 5% = 20
30% + 5% = 35%
120 + 20 = 140
So they had traveled 140 miles when Joshua fell asleep. Hope this helps :)
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