As ∠ ( 6x + 6 )° and ∠ ( 8x + 2 )° are vertically opposite angles , their measures will be equal .
Which means :-
[tex]6x + 6 = 8x + 2[/tex]
[tex]6 = 8x + 2 - 6x[/tex]
[tex]6 = 2x + 2[/tex]
[tex]2x + 2 = 6[/tex]
[tex]2x = 6 - 2[/tex]
[tex]2x = 4[/tex]
[tex]x = \frac{4}{2} [/tex]
[tex]\color{hotpink}x = 2[/tex]
Then :-
1) = ∠URS
= 6x + 6
= 6 × 2 + 6
= 12 + 6
[tex] \color{olive} ∠URS \color{hotpink} = 18°[/tex]
2) = ∠QRT
= 8x + 2
= 8 × 2 + 2
= 16 + 2
[tex]\color{olive} ∠QRT \color{hotpink}= 18°[/tex]
Therefore , the correct options are :-
[tex]\color{olive} x \color{hotpink} = \color{hotpink} \color{olive} 2[/tex]
[tex]\color{olive} ∠QRT\color{hotpink} = \color{olive} 18 \: deg[/tex]
[tex]\color{olive} ∠URS \color{hotpink} = \color{olive} 18 \: deg[/tex]
