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bazaltina [42]
4 years ago
6

Can somebody please help me solve this puzzle of parallel lines and transversals ?

Mathematics
1 answer:
expeople1 [14]4 years ago
4 0

This is crazy. Okay here I go...

m<1 = 53°

m<2 = 90° (perpendicular lines)

m<3 = 37° (forming straight angle)

m<4 = 53° (compliment with <3)

m<5 = 90° (perpendicular lines)

m<6 = 37° (compliment with <1)

m<7 = 37° (alt. int. angle pair with <6)

m<8 = 143° (linear pair with <7)

m<9 = 37° (vertical angle pair with <7)

m<10 = 143° (vertical angle pair with <8)

m<11 = 53° (alt. int. angle pair with <4)

m<12 = 127° (linear pair with <11)

m<13 = 53° (vertical angle pair with <11)

m<14 = m<15 = 63.5° (vertical angle pair with <12, split evenly among two <)

m<16, m<17, m<18, m<19 are unknown for now

m<20 = 90° (perpendicular lines)

m<18 = 37° (angles in a triangle)

m<16 = 37° (vertical angles with <18)

m<17 = 143° (linear pair with <18)

m<19 = 143° (vertical angles with <17)

m<21 = 90° (perpendicular lines)

m<24 and m<25 first!

m<24 = 90° (perpendicular lines)

m<25 = 26.5° (angles in a triangle)

m<23 = 26.5° (alt. int. angle pair with <25)

m<22 = 63.5° (compliments with <23)

m<26 = 153.5° (supplements with <25)

m<27 = 26.5° (vertical angels with <25)

m<28 = 153.5° (vertical angels with <26)

m<29 = 143° (alt. int. angle pair with <17)

m<30 = 37° (alt. int. angle pair with <18)

m<31 = 143° (vertical angles with <29)

m<32 = 37° (vertical angles with <30)

m<33 = 116.5° (angles in a triangle)

m<34 = 63.5° (linear pair with <33)

m<35 = 116.5° (vertical angles with <33)

m<36 = 63.5° (vertical angles with <34)

m<37 = 116.5° (corresponding angle with <33)

m<38 = 63.5° (corresponding angle with <34)

m<39 = 116.5° (corresponding angle with <35)

m<40 = 63.5° (corresponding angle with <36)

m<41 = 53° (angles in a triangle)

m<42 = 127° (linear pair with <41)

m<43 = 53° (vertical angles with <41)

m<44 = 127° (vertical angles with <42)

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One leg of a right triangle has a length of 77 m. the other sides have lengths that are consecutive integers. find these lengths
ANTONII [103]
Let x and x+1 represent the consecutive integers, then x is the other leg and x+1 is the hypotenuse (because the hypotenuse must be greater than its sides).

Use Pythagorean Theorem:
  a²   + b² = c²
(77)² + x² = (x+1)²
5929 + x² = x² + 2x + 1
5928        =        2x
2964        =          x

x+1 = 2965

Answer: The other leg is 2964 m and the hypotenuse is 2965 m
5 0
4 years ago
Find the measure of
koban [17]

Answer:

m∡GHI = 21°

Step-by-step explanation:

Since the lines are intersecting, GHI and JHK are opposite angles, so they are the same measure.

That means you can set them equal to each other

x + 7 = 3x - 21

x = 14

Now plug x into GHI

14 + 7 = 21

m∡GHI = 21°

7 0
4 years ago
The following figure is a Cube. Find the missing values.
Alla [95]

Answer:

384 ft²

Step-by-step explanation:

Alrighty! The volume of a cube is V = a³. The equation for the surface area of a cube is 6a². The key number here will come with finding what a is. Here, we are already given the volume: 512 ft³. By working backwards a little we can solve for the variable a using the volume.

Volume = a³

512 = a³

Here we need to isolate the variable a in order to solve for it. In order to do this we must figure out a way to move the cube³ over. We can do this by cube rooting 512!

512 = a³

∛512 = a

The cubed root of 512 = 8 thus:

8 = a

Now we that we have solved for the variable a, we can plug this into our equation for the surface area of a cube.

SA = 6a²

a = 8

SA = 6(8)²

Solving exponents comes first naturally. 8² = 64

SA = 6(64)

SA = 384

Ta-da! Your surface area is 384 ft².

3 0
3 years ago
Which sign makes this number sentence true?
Bumek [7]
Believe the answer is C
5 0
3 years ago
I need help, only answer if you know
marshall27 [118]

Answer:

Step-by-step explanation:

Light blue

5 0
3 years ago
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