Need help , due tomorrow.... will give brainliest answer if ALL done and ALL correct
1 answer:
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Answer:
60 degrees
Step-by-step explanation:
To first solve this problem, we need to figure out the size of an interior angle for a regular hexagon.
This can be done with the formula :
, with n being the number of sides
A hexagon has 6 sides so here is how we would solve for the interior angle:
, with n= 6 sides
Now that we know that each interior angle in the hexagon is 120 degrees, we can now turn our attention to the rhombus.
The opposite angles of the rhombus are congruent, so the two larger obtuse angles are congruent, and so are the two smaller acute angles.
It is also important to note that a rhombus is a quadrilateral, so all of its interior angles add up to 360 degrees.
Looking at the rhombus, we already know one of the angles because it is shared by the interior angle of the hexagon, so the two larger angles in the rhombus are both 120 degrees.
But what about the smaller angles? All we need to do is subtract the two larger angles form 360 and divide by 2 to find the angle.
, so the smaller angle in the rhombus is 60 degrees.
Now that we know both the interior angle and smaller angle of the rhombus, we can find x.
Together, angle x and the angle adjacent to it makes up an interior angle of the hexagon, so x plus that angle is going to equal to 120 degrees.
All we need to do is solve for x:
x = 60 degrees
Answer:
8) Real; Rational
9) Real; Rational; Integer; Whole; Natural
10) Real; Rational
Step-by-step explanation:
Real numbers consists of the subsets:
Irrational Numbers:
Irrational numbers is the subset complementary to rational numbers. It includes numbers such as √(2) or π. These numbers do not repeat nor terminate.
Rational Numbers:
Rational numbers are all the others. They include the integers as well as the repeating and terminating decimals.
Integers:
Integers include the entire set of whole numbers and the negative numbers. This subset does not include decimals nor fractions. Thus, the integers are: ...-3, -2, -1, 0, 1, 2, 3... etc.
Whole Numbers:
Whole numbers is the set of natural numbers that <em>includes</em> 0. So, whole numbers are: 0, 1, 2, 3... and so on.
Natural Numbers:
Natural numbers or the counting numbers are all the positive, non-decimal numbers. These are 1, 2, 3... and so on. This set does not include 0.
8)
The given number is not natural, whole, nor an integer because it is a decimal. It repeats, so it belongs to the rational numbers subset.
9)
The square root of 4 is simply 2. 2 is a natural number. Because of this, this means that 2 is also a whole number, integer, and a rational number.
10)
The given number is a fraction and it does not reduce to a whole number, so it's not a natural number, whole number, nor an integer. It does terminate, so it belongs to the rational numbers subset.