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vekshin1
3 years ago
10

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

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

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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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