Answer:
- m[tex]\angle[/tex]STW = 40°
- m[tex]\angle[/tex] TSV = 140°
Step-by-step explanation:
Here it is given that ,l ines PV , QW and RX are parallel .That is ,
[tex]\longrightarrow PV \ || \ QW \ || RX [/tex]
And we would like to find out the value of ,
[tex]\longrightarrow m\angle STW \ \& \ \angle TSV [/tex]
As we know that when a transversal intersects two parallel lines then ,
- Corresponding angles are equal .Also this is used as an axiom to prove that two lines are parallel .
- The sum of co- interior angles is 180° .
Here ,
[tex]\angle STW [/tex] and [tex]\angle TUX [/tex] are corresponding angles .So they must be equal.
[tex]\longrightarrow x = 2y \dots (i)[/tex]
Again here [tex]\angle VST[/tex] and [tex]\angle STW[/tex] are co- interior angles. So ,
[tex]\longrightarrow x + (x +5y) = 180^o \dots (ii) [/tex]
Substitute the value from equation (i) into (ii) ,
[tex]\longrightarrow 2y + 2y +5y =180^o \\[/tex]
[tex]\longrightarrow 9y = 180^o\\[/tex]
[tex]\longrightarrow y =\dfrac{180^o}{9}\\[/tex]
[tex]\longrightarrow y = 20^o [/tex]
[tex]\rule{200}4[/tex]
Therefore , we may find out the required angles as ,
[tex]\longrightarrow m\angle STW = x \\ [/tex]
[tex]\longrightarrow m\angle STW = 2y\\ [/tex]
[tex]\longrightarrow m\angle STW = 2(20^o)\\ [/tex]
[tex]\longrightarrow \underline{\underline{m\angle STW = 40^o}} [/tex]
[tex]\rule{200}4[/tex]
Again ,
[tex]\longrightarrow m\angle TSV = x + 5y \\ [/tex]
[tex]\longrightarrow m\angle TSV = 40^o 5(20^o)\\[/tex]
[tex]\longrightarrow m\angle TSV = 40^o + 100^o\\ [/tex]
[tex]\longrightarrow \underline{\underline{ m\angle TSV = 140^o }} [/tex]
And we are done!
[tex]\rule{200}4[/tex]
