To fill in the missing angle and side measurements for the similar triangles △OYS and △TER (where △OYS is similar to △TER), we need to apply the properties of similar triangles, which tell us that corresponding angles are equal and the ratios of corresponding sides are equal.
Assuming the side measurements correspond to the sides opposite the angles in the order given, we need to find the missing values. Typically, we know at least one angle and one side from each triangle or specific ratios, but without explicit relationships or corresponding angles/sides given in your problem, I cannot assign the numbers precisely.
However, I'll outline how to approach this if you had specific pairs:
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Identify the known angles and sides from both triangles. Let's say:
- In △OYS, angle O has measure = 40°, side OY = 100, side OS = 33, etc.
- In △TER, angle T corresponds to angle O, side TE corresponds to OY, and so on.
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Use the fact that if the triangles are similar, then:
- \( \frac{side\ OY}{side\ TE} = \frac{side\ OS}{side\ ER} = \frac{side\ YS}{side\ TR} \)
- The angles should match up as well.
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The missing angles can be calculated based on the fact that the sum of angles in a triangle is 180°.
For example, if you knew one angle in each triangle, you could subtract from 180° to find the third angle.
- Once you establish the proportions and relationships, you will input the corresponding values as given.
For a specific numerical example: Assuming you know \( OY = 100 \), you could find corresponding \( TE \) as follows: If matching sides are in the same ratio:
- If \( \frac{100}{TE} = \frac{33}{ER} \) then you could solve for \( TE \) if \( ER \) is known.
Without specific correspondence data or context for your problem, this is the general method to find the missing angle and side measurements. If you provide the specific relationships of the angles and sides, I can assist further!
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