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find the value of x and the m/_TSUvalue of x:m/_TSU =

Find The Value Of X And The MTSUvalue Of XmTSU class=

Sagot :

Answer:

• x=7

,

• m∠TSU =89 degrees

Explanation:

From the diagram:

Angles STU and TUS are opposite interior angles of angle TSW.

We know that 'the sum of the two opposite interior angles is equal to the exterior angle'.

Therefore:

[tex]m\angle\text{TSW}=m\angle STU+m\angle\text{TUS}[/tex]

Substituting the given values, we have:

[tex]\begin{gathered} 12x+7=5x-1+57^0 \\ 12x-5x=57-1-7 \\ 7x=49 \\ x=\frac{49}{7} \\ x=7 \end{gathered}[/tex]

The value of x is 7.

Angles TSW and TSU are linear pairs. First, we find the value of TSW.

[tex]\begin{gathered} \angle\text{TSW}=12x+7 \\ =12(7)+7 \\ =84+7 \\ =91^0 \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} m\angle\text{TSU}=180-91 \\ =89^0 \end{gathered}[/tex]

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