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3 years ago

In the rhombus, m∠1 = 40°. Find m∠2.

Mathematics

1 answer:

den301095 [7]3 years ago

5 0

Answer:

Option C is correct.

Step-by-step explanation:

Given: A rhombus. m∠1 = 40°

To find: m∠2

We know that Rhombus is a parallelogram with all equal sides.

⇒ Opposite sides of the Rhombus are parallel.

Then Diagonal act as a traversal for parallel sides.

So, m∠2 = m∠1 ( Alternate Interior Angles are equal )

m∠2 = 40°

Therefore, Option C is correct.

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How do you find the arctan 4/3 ? (Without a calculator)

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2 years ago

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3 years ago

Evelyn can run 3 miles in 40 minutes. Which equation can be solved to find m, the number of miles Evelyn can run in 60 minutes?

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Answer:

m= 4.5 miles

Step-by-step explanation:

Let the number of miles Evelyn can run be m and can be modeled by the equation below

m= kx

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2 years ago

Please show work and thank youuu

Assoli18 [71]

Answer: $6\sqrt{3}$

======================================================

Explanation:

Method 1

We can use the pythagorean theorem to find x.

$a^2+b^2 = c^2\\\\6^2+x^2 = 12^2\\\\36+x^2 = 144\\\\x^2 = 144-36\\\\x^2 = 108\\\\x = \sqrt{108}\\\\x = \sqrt{36*3}\\\\x = \sqrt{36}*\sqrt{3}\\\\x = 6\sqrt{3}\\\\$

-----------------------------------

Method 2

Use the sine ratio to find x. You'll need a reference sheet or the unit circle, or simply memorize that sin(60) = sqrt(3)/2

$\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(60^{\circ}) = \frac{x}{12}\\\\\frac{\sqrt{3}}{2} = \frac{x}{12}\\\\x = 12*\frac{\sqrt{3}}{2}\\\\x = 6\sqrt{3}\\\\$

-----------------------------------

Method 3

Similar to the previous method, but we'll use tangent this time.

Use a reference sheet, unit circle, or memorize that tan(60) = sqrt(3)

$\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(60^{\circ}) = \frac{x}{6}\\\\\sqrt{3} = \frac{x}{6}\\\\x = 6\sqrt{3}\\\\$

-----------------------------------

Method 4

This is a 30-60-90 triangle. In other words, the angles are 30 degrees, 60 degrees, and 90 degrees.

Because of this special type of triangle, we know that the long leg is exactly sqrt(3) times that of the short leg.

$\text{long leg} = (\text{short leg})*\sqrt{3}\\\\x = 6\sqrt{3}\\\\$

The short leg is always opposite the smallest angle (30 degrees).

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2 years ago