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In the rectangle below, SU= 4x – 2, RT = 5x-10, and m Z VSR=26°.Find RV and m ZVTS.Rm

In The Rectangle Below SU 4x 2 RT 5x10 And M Z VSR26Find RV And M ZVTSRm class=

Sagot :

SU and RT are the diagonals of the rectangle and are thus equal.

We the equate them to find x

SU = RT = 4x - 2 = 5x - 10

subtracting 4x from both sides gives:

4x - 2 - 4x = 5x - 10 - 4x

-2 = x - 10

Adding 10 to both sides give:

10 - 2 = x - 10 + 10

x = 8

RV is half of RT

where = RT = 4(8) - 2 = 32 - 2 = 40

Therefore, RV = 40/2 = 20

To calculate angle VTS, we consider that it is in an isosceles triangle with its angle equal to angle VST. Same angle VST is complementary with angle VSR

Therefore, angle VTS = VST = 90 - 26 = 64 degrees (sum of angles in a right angle)

VTS = 64 degrees

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