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3 years ago

List the angles of the given triangle from smallest to largest. Explain your reasoning. Solve for x.

Mathematics

1 answer:

julia-pushkina [17]3 years ago

7 0

Answer:

Smallest to Largest: Angle ACD, Angle ADC, Angle CAD, Angle ACB

Step-by-step explanation:

To find the angles, let's first solve for x.

Let's call the missing side angle ACD= y

We know that there are 180 degrees in a triangle. So we can write the equation,

6x+4+(4x-2)+y= 180

and, We know that angle ACB is a linear pair with angle ACD, so both angles would add up to 180 degrees. We can write the equation,

9x+16+y=180

Let's now solve for x with both of these equations using elimination.

Simplify the equations,

6x+4+(4x-2)+y= 180 -> 10x+y=178

9x+16+y=180 -> 9x+y=164

-1(10x+y=178) -> -10x-y=-178

-10x-y=-178

9x+y=164

-x= -14

x= 14

Now that we have solved for x, we can find the missing angles.

Angle ACB= 9x+16 -> 9(14)+16= 142 degrees

Angle CAD= 6x+4 -> 6(14)+4= 88 degrees

Angle ADC= 4x-2 -> 4(14)-2= 54 degrees

Angle ACD= 180-(Angle CAD+ Angle ADC) -> 180-(88+54)= 38 degrees

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NO. Three congruent angles only proves the triangles are similar. You must have at least one side length to prove congruency.

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Answer: C

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3 years ago

Read 2 more answers

How to simplify <br><br> 9m3+5m2+5m3-3m3+4m4+8m

tamaranim1 [39]

Answer:

$4m^4+11m^3 + 5m^2 + 8m$

Step-by-step explanation:

I take it that the expression is

$9m^3+5m^2+5m^3-3m^3+4m^4+8m$

Collect like terms and add the coefficients

$4m^4+(9m^3+5m^3-3m^3) + 5m^2 + 8m$

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2 years ago

(j + 1)(2) simplify the expression

andrey2020 [161]

Answer:

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Step-by-step explanation:

Multiply both parts of the equation by 2 to get your answer.

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4 years ago

Find the center and the radius of this equation by completing the

Colt1911 [192]

Answer:

$x^2 +4x +(4/2)^2 +y^2 -20 y +(20/2)^2 +100 = (4/2)^2 +(20/2)^2$

And solving we got:

$x^2 +4x+ 4 +y^2 +20y +100 +100 = 4 +100$

If we subtract 100 from both sides we got:

$(x+2)^2 +(y+10)^2 = 4$

$C= (-2,-10)$

$r = \sqrt{4}=2$

Step-by-step explanation:

For this case we have the following equation given:

$x^2 +4x +y^2 -20 y +100=0$

We want to find a general expression given by:

$(x-h)^2 +(y-k)^2 = r^2$

Where the center is (h.k) and the radius is r.

We can begin completing the squares of the equation given and we got:

$x^2 +4x +(4/2)^2 +y^2 -20 y +(20/2)^2 +100 = (4/2)^2 +(20/2)^2$

And solving we got:

$x^2 +4x+ 4 +y^2 +20y +100 +100 = 4 +100$

If we subtract 100 from both sides we got:

$(x+2)^2 +(y+10)^2 = 4$

Then we can conclude that the center is:

$C= (-2,-10)$

And the radius would be:

$r = \sqrt{4}=2$

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3 years ago

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Answer:
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3 years ago