two horizontal lines are cut by a transversal. what is the least number of angle measures you need to know in order to find the
measure of every angle? explain your reasoning
1 answer:
Answer: The answer is only one angle. Explained.
Step-by-step explanation: As given in the question and shown in the attached figure, the lines horizontal lines 'p' and 'q' are cut by the transversal 'r'. We need to determine the least number of angles among the eight angles mentioned in the figure to find the measure of all the angles.
Suppose, the measure of ∠1 is given as x°.
So, ∠2 = 180° - x (linear pair of angles),
∠3 = x (=∠1, vertically opposite angles),
∠4 = 180° - x (=∠2, verticaly opposite angles),
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, ∠4 = ∠8. These are pairs of correspomding angles.
Thus, we need the measure of only one angle to find the measure of all the angles.
Hence explained.
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Answer:
The correct option is 3.
Step-by-step explanation:
From the given graph it is noticed that the related line passing through the point (-3,1) and (0,3).
If a line passing through two points, then the equation of line is
The equation of related line is
Add 1 on both the sides.
The equation of related line is .
The related line is a dotted line, it means the point on the line does not included in the solution set.
The shaded region is above the line so the sign of inequity is >.
The required inequality is
Therefore option 3 is correct.
It is given that two vertices of square are (0,0) and (4,2).
Now the problem is that you haven't given that whether these two vertices are adjacent vertices or opposite vertices of the square.
1. By Supposing that these two are adjacent vertices of Square
The third vertex will be at (-4,2) which lies in third quadrant.
Suppose the coordinate of fourth vertex be (x,y).
Mid point of line joining (4,2) and (-4,2) is{ [4+(-4)]/2,(2+2)/2} is (0,2).
Mid point of line joining (x,y) and (0,0) is (x/2,y/2).
Since diagonals of square bisect each other,
∵ x/2=0
⇒x=0
and
y/2=2
⇒y=4
So, The Coordinate of fourth vertex is (0,4).
Now coming back to second condition if these are two opposite vertex of Square.
Let the third coordinate be (a,b).
Length of diagonal=
Now,let side of Square be A.
Then length of Diagonal of square =√2 A
⇒√2 A=2√5
⇒A =√10
As third vertex is (a,b).
Using distance formula
a² + b²=10 -------------(1)
(a-4)²+ (b-2)²=10 --------------(2)
Solving expression (1) and (2), we get
⇒a²+ b²=(a-4)² +(b-2)²
⇒2a + b =5
⇒b=5-2a
Putting the value of b in (1),we get
⇒a² +(5-2a)²=10
⇒a²+25+4a²-20a =10
⇒5a²-20a+15=0
⇒a² - 4a + 3=0
Splitting the middle term,we get
⇒(a-3)(a-1)=0
⇒a=3 ∧ a=1
we get b=5-2×1=3 and b=5-2×3=5-6=-1
So,the other vertex are (1,3) and(3,-1).
