I don't understand what to do. (angle measures & side proportions) | Mathematics | Page 1

analog crystalBOT Dec 17, 2024, 2:40 AM

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ornate mountain Dec 17, 2024, 2:46 AM

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For the side proportions, it is literally asking you to find the

given ratios as simplified fractions. For example::
\begin{align*} \frac{AC}{ZX} &= \frac{10}{7.5} \ &= \frac{10}{7.5} \times \frac{2}{2} \ &= \frac{20}{15} \ &= \frac{4}{3} \end{align*}

winter plumeBOT Dec 17, 2024, 2:46 AM

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Jay

ornate mountain Dec 17, 2024, 2:47 AM

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The angle $\angle{VXZ}$ can be found using the fact that the angle sum of a triangle is $180^\circ$

winter plumeBOT Dec 17, 2024, 2:47 AM

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Jay

jovial bronze Dec 17, 2024, 2:50 AM

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i did the same steps for the side proportions

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they're all 4/3? right

jovial bronze Dec 17, 2024, 2:51 AM

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winter plume **Jay**

What do you mean by this

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180 minus whichever angle measure?

ornate mountain Dec 17, 2024, 2:55 AM

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jovial bronze What do you mean by this

In $\Delta VXZ$, we know that $\angle{VXZ} + \angle{XZV} + \angle{ZVX} = 180^\circ$

as the angle sum of any triangle is $180^\circ$, yes?

And we know that $\angle{XZV} = 27^\circ$ and that $\angle{ZVX} = 22^\circ$.

You can put these two pieces of information into the above equation

which will now have a single unknown, $\angle{VXZ}$, and you can

solve the equation to find the size of this angle.

winter plumeBOT Dec 17, 2024, 2:56 AM

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Jay

ornate mountain Dec 17, 2024, 2:57 AM

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jovial bronze they're all 4/3? right

I expected that they would be the same... what does this mean about the relationship between the two triangles? Hw does this help you to solve the rest of the question?

jovial bronze Dec 17, 2024, 3:00 AM

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so 180 minus the two other angles

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to find the unknown

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wait no

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this is what i have

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im unsure if i have CAF and CFA swapped incorrectly though

ornate mountain Dec 17, 2024, 3:08 AM

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The ratios tell you that AC corresponds to ZX and AF corresponds to ... ?

jovial bronze Dec 17, 2024, 3:08 AM

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eachother?

ornate mountain Dec 17, 2024, 3:08 AM

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Because the angle between AC and AF will correspond to the angle between ZX and whichever side corresponds to AF

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The first ratio was AC / ZX, meaning that this pair of sides is corresponding

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Which ratio has AF in it? hence, which side corresponds to AF?

jovial bronze Dec 17, 2024, 3:10 AM

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VZ?

ornate mountain Dec 17, 2024, 3:10 AM

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Yes

jovial bronze Dec 17, 2024, 3:11 AM

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thats what I looked too

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So im correct ?

ornate mountain Dec 17, 2024, 3:11 AM

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So, the angle you want is between AC and AF... so, the corresponding angle is between ...?

jovial bronze Dec 17, 2024, 3:12 AM

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CAF?

ornate mountain Dec 17, 2024, 3:15 AM

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CAF is the angle you want, yes... it is between CA and AF... the sides corresponding to CA and AF in triangle VXZ are ... ?

jovial bronze Dec 17, 2024, 3:15 AM

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AC - ZX

ornate mountain Dec 17, 2024, 3:16 AM

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And AF corresponds to VZ, you said so above

jovial bronze Dec 17, 2024, 3:16 AM

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FA - VZ

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Yes

ornate mountain Dec 17, 2024, 3:16 AM

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Yes

jovial bronze Dec 17, 2024, 3:16 AM

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so as they correspond to eachother are my degrees correct?

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they seem the same

ornate mountain Dec 17, 2024, 3:16 AM

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so you want the angle between ZX and VZ

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so yes, you are correct

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I was trying to get you to express the reasoning

#I don't understand what to do. (angle measures & side proportions)