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TV−→− bisects ∠RTS. If the m∠RTV=(16x−6)° and m∠VTS=(13x+9)° , what is the value of x and the m∠RTV ?
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Answer :

MrRoyal

Answer:

[tex]x = 5[/tex]

[tex]RTV = 74[/tex]

Step-by-step explanation:

Given

[tex]RTV=16x - 6[/tex]

[tex]VTS=13x+9[/tex]

Required

Determine the values of x and RTV

Since, TV is a bisector, then

[tex]RTS = RTV + VTS[/tex] --- (1)

and

[tex]RTV = VTS[/tex] -- (2)

Substitute values of RTV and VTS in (2)

[tex]16x - 6 = 13x + 9[/tex]

Collect Like Terms

[tex]16x - 13x = 9 + 6[/tex]

[tex]3x = 15[/tex]

Solve for x

[tex]x = 5[/tex]

Substitute 5 for x in [tex]RTV=16x - 6[/tex]

[tex]RTV = 16 * 5 - 6[/tex]

[tex]RTV = 80 - 6[/tex]

[tex]RTV = 74[/tex]

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