PENTALIZARD2834
04.11.2019 •
Mathematics
What is the value of x?
42
22
38
5
Solved
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Ответ:
38
Step-by-step explanation:
since the sum of all three interior angles in a triangles makes 180° :
3x - 16 + x + x + 6 = 180
5x -10 = 180
5x = 190
x = 38
Ответ:
38°
Step-by-step explanation:
In a triagle the sum of all the internal angles must be equal to 180°, so we have to sum 3x-16 and x+6 and x:
Now we put togehter like terms, this is: we sum the terms with x:
and the independent terms on the left side:
so the equation becomes:
and we clear for x:
the value of x is 38°
Ответ:
Prove that all sides are congruent, and the slopes of consecutive sides are opposite reciprocals ⇒ First answer
Step-by-step explanation:
* Lets revise the properties of the square
- In the square every two opposite sides are parallel
- In the square all sides are equal
- In the square the four angles are right angles
- In the square every two adjacent sides have opposite reciprocal slopes
- In the square the diagonals are equal and perpendicular
* So to prove the quadrilateral is a square you must have two conditions
from the statements above
- Every to opposite sides parallel and two consecutive sides are equal
- The four sides are equal and each two consecutive sides are ⊥
- Its diagonals are equal and perpendicular
* Lets check which statement is right and prove it
# First
- Prove that all sides are congruent, and the slopes of consecutive
sides are opposite reciprocals
∵ The meaning of the slopes of consecutive sides are opposite
reciprocals is the consecutive sides are ⊥, because the slopes
of the ⊥ segments are opposite reciprocal
- Lets prove this statement
- In quadrilateral ABCD
∵ A = (-3 , 5) , B = (1 , 7) , C = (3 , 3) , D = (-1 , 1)
∵ The length of the segment whose endpoints are (x1 , y1) , (x2 , y2)
is √[(x2 - x1)² + (y2 - y1)²]
∴ AB = √[(1 - -3)² + (7 - 5)²] = √[(4)² + (2)²] = √[16 + 4] = √20
∴ BC = √[(3 - 1)² + (3 - 7)²] = √[(2)² + (-4)²] = √[4 + 16] = √20
∴ CD = √[(-1 - 3)² + (1 - 3)²] = √[(-4)² + (-2)²] = √[16 + 4] = √20
∴ AD = √[(-1 - -3)² + (1 - 5)²] = √[(2)² + (-4)²] = √[4 + 16] = √20
∴ The four sides are congruent ⇒ (1)
∵ The slope of the segment whose endpoints are (x1 , y1) , (x2 , y2)
is
∴ The slope of
∴ The slope of
∴ The slope of
∴ The slope of
- From above
∵ The AB and BC are consecutive sides
∵ Their slopes are 1/2 , -2 ⇒ opposite reciprocal
∵ The BC and CD are consecutive sides
∵ Their slopes are -2 , 1/2 ⇒ opposite reciprocal
∵ The CD and DA are consecutive sides
∵ Their slopes are 1/2 , -2 ⇒ opposite reciprocal
∵ The DA and AB are consecutive sides
∵ Their slopes are -2 , 1/2 ⇒ opposite reciprocal
∴ The slopes of consecutive sides are opposite reciprocals ⇒ (2)
- From (1) and (2) the first statement is true
* Prove that all sides are congruent, and the slopes of consecutive
sides are opposite reciprocals