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dreawongdga
14.05.2021 •
Mathematics
In the rectangle below, SU= 4x-2, RT = 5x-10, and m ZSVT= 84º.
Find RV and m ZVUR.
R
S
U
T
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Ответ:
RV = 15, ∠ VUR = 48°
Step-by-step explanation:
The diagonals of a rectangle are congruent , so
RT = SU , that is
5x - 10 = 4x - 2 ( subtract 4x from both sides )
x - 10 = - 2 ( add 10 to both sides )
x = 8
Then
RT = 5x - 10 = 5(8) - 10 = 40 - 10 = 30
The diagonals bisect each other , then
RV = 0.5 × 30 = 15
---------------------------------------------------------------
∠ RVU = ∠ svt = 84° ( vertical angles )
RV = UV ( diagonals are congruent and bisect each other )
Then Δ RVU is isosceles with base angles congruent , then
∠ VUR =
=
= 48°
Ответ:
30 degrees is your correct answer.
Step-by-step explanation: