Using the vertical angle image from problem 1, let ∠2 = 4x-4 and ∠4 = x+50.
A. What is the value of x?
B. What is the measure of ∠2?
C. Find the measure of ∠3.
Answers
Answer:
A) x = 18, B) ∠2 = 68°, C) ∠3 = 112°Step-by-step explanation:
According to vertical angles theorem, when two lines intersect the opposite angles are equal and adjacent angles are supplementary.
Given∠2 = 4x-4 and ∠4 = x+50A) Find the value of x:
4x - 4 = x + 504x - x = 50 + 43x = 54x = 54/3x = 18B) Find the measure of angle 2:
∠2 = 4*18 - 4 = 72 - 4 = 68C) Angles 2 and 3 are supplementary so their sum is 180°.
∠2 + ∠3 = 18068 + ∠3 = 180∠3 = 180 - 68∠3 = 112°Answer:
A. x = 18
B. m∠2 = 68°
C. m∠2 = 112°
Step-by-step explanation:
Given:
[tex]\angle 2=4x-4[/tex][tex]\angle4=x+50[/tex]Part AVertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Therefore:
[tex]\implies \angle 2 = \angle 4[/tex]
[tex]\implies 4x-4= x+50[/tex]
[tex]\implies 4x-4-x= x+50-x[/tex]
[tex]\implies 3x-4= 50[/tex]
[tex]\implies 3x-4+4= 50+4[/tex]
[tex]\implies 3x=54[/tex]
[tex]\implies 3x\div 3=54 \div 3[/tex]
[tex]\implies x=18[/tex]
Part BTo find the measure of ∠2, substitute the found value of x into the given expression for ∠2:
[tex]\implies m\angle 2 =(4x-4)^{\circ}[/tex]
[tex]\implies m\angle 2 =[4(18)-4]^{\circ}[/tex]
[tex]\implies m\angle 2 =(72-4)^{\circ}[/tex]
[tex]\implies m\angle 2 =68^{\circ}[/tex]
Part CAngles on a straight line sum to 180°:
[tex]\implies m\angle 2 +m\angle 3=180^{\circ}[/tex]
[tex]\implies 68 ^{\circ}+m\angle 3=180^{\circ}[/tex]
[tex]\implies m\angle 3=180^{\circ}-68 ^{\circ}[/tex]
[tex]\implies m\angle 3=112 ^{\circ}[/tex]
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Answers
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Answers
Answer:
83 deg
Step-by-step explanation:
sum of angles in triangle = 180
<1=180-(31+66)=180-97=83
Answer:
83 degrees
Step-by-step explanation:
the angles in a triangle add up to 180 degrees
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Answer:
16.1 seconds
Step-by-step explanation:
h = 16t²
h = 4144
4144 = 16t²
÷16 ÷16
----------------
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√259 = √t²
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Answers
Answer:
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Step-by-step explanation:
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[tex]f(x)=-x+2[/tex]
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Answers
Juan bought 4.5 lbs for $7.98 per lb
This implies that 1 lb is sold at the rate of $7.98
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4.5lb ------ $x
Introduce cross multiplication
1 * x = 7.98 x 4.5
x = $35.91
Therefore, 4.5lbs is sold at the rate of $35.91
The tax sales is 6%
Total amount = original price + 6% of original price
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= $38.0646
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Answers
Remember the following kinds of triangles:
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-Right triangle: Has one angle that measures exactly 90º.
-Obtuse triangle: Has one angle greater than 90º.
By sides:
- Equilateral triangle: Has three equal sides.
- Isosceles triangle: has two equal side and one side different from the others.
- Scalene triangle: has no equal sides.
Since larger sides are opposite to larger angles, then, a triangle with angle measures of 66º, 82º and 32º cannot have equal sides (they should be opposite to equal angles).
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Answers
Answer:
3x+2=8
X=2
Step-by-step explanation:
3x+2=8
3x=6
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Answers
Total number of eggs = 6 + 19 + 14 + 11 + 23 + 2 = 75 eggs
Total hatched eggs = 6 + 14 + 23 = 43
[tex]\begin{gathered} \text{Percentage of eggs hatched = }\frac{43}{75}\times100\text{ } \\ \text{= 57.33 }\approx\text{ 57} \end{gathered}[/tex]Therefore, the answer is 57 ( to the nearest whole number)
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In order to determine if their corresponding sides are in proportion, you can set up this equation:
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Answers
Answer:
35 meters.
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Answers
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Answers
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Answers
Given :
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The rule of reflection across the line y = x will be :
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Q = ( 5 , -6 ) , Q' = ( -6 , 5 )
R = ( -2 , 6 ) , R ' ( 6 , -2 )