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.
So first find the area
area=legnth times width
area=5/6 times 1/6
5/6 times 1/6=5/36
area=5/36 square units
tile=side legnth 1/6
area of tile=legnth times width or legnth times legnth
1/6 times 1/6=1/36
we must find how many times 1/36 goes into 5/36
divide 5/36 by 1/36
5/36 divided by 1/36=5/36 times 36/1=5/1 times 36/36=5/1 times 1=5
the answer is 5 unit squares needed to tile
Answer:
90°-33°=57°
57=2x+1
-1. -1
56=2x divide both sides by 2
28=x
x =28
1st number: 0
2nd number: 17
Answer
Step-by-step explanation:
3x+2y=34 x is the first number, y is the second.
1/2x+2y=34 multiply each number by two to get rid of the integer by the variable x.
x+4y=68 solve for x.
x=68-4y add this into the first equation to solve for variable y.
3(68-4y)+2y=34 solve for y.
204-10y=34
-10y= -170
y=17
now to solve for x
x= 68-4(17)
x= 0
