Answer:
14. ∠UVS = 63.6°
15. ∠TWU = 90°
16. ∠TUV = 116.4°
17. UW = √111 ≈ 10.5
18. SU = 2√111 ≈ 21.1
19. VT = 34
Step-by-step explanation:
The relevant relations for a rhombus are ...
- diagonals bisect each other at right angles, dividing the figure into 4 congruent right triangles
- the diagonals bisect the vertex angles
- adjacent vertex angles are supplementary
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14.
Angle UVS is double the measure of angle UVW. 2×31.8° = 63.6°.
angle UVS = 63.6°
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15.
As we said above, the angles where the diagonals cross are right angles.
angle TWU = 90°
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16.
Angle TUV is supplementary to angle UVS. 180° -63.6° = 116.4°
angle TUV = 116.4°
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17.
UW is found using the Pythagorean theorem.
UW² +TW² = TU²
UW² = TU² -TW² = 20² -17² = 111
UW = √111 ≈ 10.536
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18.
The whole diagonal is twice the measure of half of it. SU = 2×UW
SU = 2√111 ≈ 20.071
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19.
The whole diagonal is twice the measure of half of it. 2×17 = 34
VT = 34
