Answer:
1. m ∠ 1 = 113°
2. m ∠ 2 = 67°
3. m ∠ 4 = 67°,
4. m ∠ 5 = 113°
5. m ∠ 6 = 67°
6. m ∠ 7 = 113°
7. m ∠ 8 = 67°
Step-by-step explanation:
Given AB║CD and m║n and m∠3=113°
Solution, since m and n are parallel lines so AB and CD are transversal lines.
So ∠2 and ∠3 makes a linear pair whose sum is equal to 180°.
(∠2 and ∠8),(∠3 and ∠7),(∠1 and ∠5),(∠4 and ∠6) are alternate interior angles.
(∠2 and ∠4),(∠1 and ∠3),(∠5 and ∠7),(∠6 and ∠8) are corresponding angles.
When two lines are parallel and their is a transversal line then the measure of alternate angles are equal and also the measure of corresponding angles are equal.
![m\angle 2 + m\angle 3 = 180\\m\angle 2 + 113 = 180\\m\angle2=180-113=67\\m\angle2=m\angle8=67 \ (alternate\ interior\ angle)\\m\angle3=m\angle7=113 \ (alternate\ interior\ angle)\\m\angle3=m\angle1=113 \ (corresponding\ angle)\\m\angle2=m\angle4=67 \ (corresponding\ angle)\\m\angle4=m\angle6=67 \ (alternate\ interior\ angle)\\m\angle1=m\angle5=113 \ (alternate\ interior\ angle)](https://tex.z-dn.net/?f=m%5Cangle%202%20%2B%20m%5Cangle%203%20%3D%20180%5C%5Cm%5Cangle%202%20%2B%20113%20%3D%20180%5C%5Cm%5Cangle2%3D180-113%3D67%5C%5Cm%5Cangle2%3Dm%5Cangle8%3D67%20%5C%20%28alternate%5C%20interior%5C%20angle%29%5C%5Cm%5Cangle3%3Dm%5Cangle7%3D113%20%5C%20%28alternate%5C%20interior%5C%20angle%29%5C%5Cm%5Cangle3%3Dm%5Cangle1%3D113%20%5C%20%28corresponding%5C%20angle%29%5C%5Cm%5Cangle2%3Dm%5Cangle4%3D67%20%5C%20%28corresponding%5C%20angle%29%5C%5Cm%5Cangle4%3Dm%5Cangle6%3D67%20%5C%20%28alternate%5C%20interior%5C%20angle%29%5C%5Cm%5Cangle1%3Dm%5Cangle5%3D113%20%5C%20%28alternate%5C%20interior%5C%20angle%29)
Hence the measure of all angles are:
1. m ∠ 1 = 113°
2. m ∠ 2 = 67°
3. m ∠ 4 = 67°,
4. m ∠ 5 = 113°
5. m ∠ 6 = 67°
6. m ∠ 7 = 113°
7. m ∠ 8 = 67°
A scatterplot is used to represent a correlation between two variables. There are two types of correlations: positive and negative. Variables that are positively correlated move in the same direction, while variables that are negatively correlated move in opposite directions.
Step-by-step explanation:
You have 3/5 of an apple pie" means you have 3 pieces of the 5-piece pie
"You divide the remaining pie into 5 equal slices." means
(3/5 pie) / 5
The math:
(3/5 pie) / 5
is also
(3/5 pie) * (1/5) [to divide by fraction 5/1, invert to 1/5 and multiply]
is also (1/5) * (3/5 pie)
[This means 1/5 of the 3/5 of a pie that is left of"]
So,
each slice is (1/5)*(3/5) pie = 3/25 pie [multiply numerators and denominators]
These ones always feel weird. But we will read the problem directly and do what it says.
So it is 3/5 divided by 5.
Or 3/5/5.
But that looks really weird, so lets think of it like multiplying by 1/5 instead (which is the same as dividing by 5)
So, (3/5) * (1/5) which equals 3/25.
Everyone gets 3 twenty fifths of a pie.
First, you try to make sure that both the denominators are the same. In order to do this, you multiply both fractions' numerator and denominator by the other fraction's denominator. Next, you combine like terms in the numerator, and then you simplify the fraction.
Answer:
Step-by-step explanation:
Rule: never completely trust a diagram that comes with a geometry question. This is a case in point. The "tiny" square is actually much larger than the "larger" square.
If you are trying to find the length of the sides of the squares, the formula is
Area = side^2
3025 = side^2
Take the square root of both sides.
sqrt(3025) = sqrt(side^2)
To find the square root of 3025, do the following
Press √
type in 3025
type in =
You should get 55.
======================
The second square is done the same way
√
90.75
=
And you should get 9.526