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

Find the value of x and the m/_TSUvalue of x:m/_TSU =-example-1
User Sok Pomaranczowy
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1 Answer

9 votes
9 votes

Answer:

• x=7

,

• m∠TSU =89 degrees

Step-by-step 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:


m\angle\text{TSW}=m\angle STU+m\angle\text{TUS}

Substituting the given values, we have:


\begin{gathered} 12x+7=5x-1+57^0 \\ 12x-5x=57-1-7 \\ 7x=49 \\ x=(49)/(7) \\ x=7 \end{gathered}

The value of x is 7.

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


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

Therefore:


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

User Hgwhittle
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