Question

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

Answer 1

• 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}`