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3 years ago

A figure with parallel lines m and n is shown. What is the measure, in degrees, of angle b?

Mathematics

1 answer:

Radda [10]3 years ago

3 0

Answer:

48°

Step-by-step explanation:

Not sure if you've learner this yet, but the two angles shown are called alternate exterior angles. To make it a little bit easier, 48° has to be the answer since it's the only other angle shown. But to explain it more..

There's corresponding and vertical angles which can be used to solve this equation. There are four spots that would equal 48°, including "b". Corresponding angles are in the same spot, but different sections. There's also vertical angles, which are right across from each other. If you apply vertical and corresponding angles b will be 48°.

Please let me know if you don't really understand what I attempted to explain. If you haven't gone into depths about what I talked about, just think about the first paragraph/section.

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Zepler [3.9K]

1/2 I guess I don't think you typed in the question correctly. Not trying to be mean.

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4 years ago

The area of the rhombus is 540 cm2; the length of one of its diagonals is 4.5 dm. What is the distance between the point of inte

malfutka [58]

1. The area of the rhombus can be found by the formula

$A=\dfrac{d_1\cdot d_2}{2},$ where $d_1,\ d_2$ are rhombus's diagonals.

Note that $d_1=4.5\ dm=45\ cm,$ then

$540=\dfrac{45\cdot d_2}{2},\\ \\540\cdot 2=45d_2,\\ \\d_2=24\ cm.$

2. The diagonals of rhombus are perpendicular and are bisectors of each other. Then the triangle formed with halfs of diagonals is right triangles with legs

$\dfrac{d_1}{2}=22.5\ cm,\ \dfrac{d_2}{2}=12\ cm.$

The hypotenuse of this triangle is the rhombus's side. By the Pythagorean theorem

$\text{rhombus's side}^2=(22.5)^2+12^2=506.25+144=650.25,\\ \\\text{rhombus's side}=25.5\ cm.$

3. The distance between the point of intersection of the diagonals and the side of the rhombus is the height of right triangle considered above.

Use twice the Pythagorean theorem to find this height:

$\left\{\begin{array}{l}x^2+h^2=12^2\\(25.5-x)^2+h^2=22.5^2,\end{array}\right.$

where x is projection of leg 12 cm and h is height.

Subtract the first equation from the second:

$(25.5-x)^2+h^2-x^2-h^2=22.5^2-12^2,\\ \\650.25-51x=506.25-144,\\ \\51x=650.25-362.25=288,\\ \\x=\dfrac{96}{17}\ cm.$

Then

$h^2=144-\left(\dfrac{96}{17}\right)^2=144-\dfrac{9216}{289}=\dfrac{32400}{289},\\ \\h=\dfrac{180}{17}\ cm.$

Answer: $h=\dfrac{180}{17}\ cm.$

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3 years ago

Read 2 more answers

Michelle is on a secret mission to reclaim artifacts that were recently stolen from the National Museum. The artifacts are locat

kolezko [41]

Answer:

scroll down

Step-by-step explanation:

basically each 3 units is 18 meters so 6 meters=1 unit

its 60 by 30 which means

10 units by 5 units

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3 years ago

Please help, I would appreciate it thank you :)

Inessa [10]

Answer:

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4 years ago

A cube's side measures 6xy inches whet is the volume

liubo4ka [24]

For a cube, $V = s^3.$

The volume is the cube of the side length.

$V = s^3$

$V = (6x^6y^8)^3$

To raise a product to an exponent, raise each factor to the exponent.

$V = (6^3) \times (x^6)^3 \times (y^8)^3$

To raise a power to a power, multiply powers.

$V = 216x^{18}y^{24}$

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4 years ago