Answer:
[tex] \huge{ \boxed{ \bold{ \tt{m \angle \: abc \: = 35 \degree}}}}[/tex]
Option C is the best choice.
Step-by-step explanation:
✺ First , Let's know about Corresponding angles :
- A pair of interior and exterior angles which lies to the same side of a transversal.
- Remember that the corresponding angles are always equal.
- The easiest way to think of corresponding angles is the 'F - Pattern'.
✎ Now, In our case , x ° and ( 3x - 70 ) ° are corresponding angles. Set up an equation and solve for x.
[tex] \sf{x = 3x - 70\: ( \: being \: corresponding \: angles})[/tex]
[tex] \longrightarrow{ \sf{x - 3x = - 70}}[/tex] { Move 3x to left hand side and change it's sign )
[tex] \longrightarrow{ \sf{ - 2x = - 70}}[/tex] { Combine like terms }
[tex] \longrightarrow{ \sf{ \frac{ - 2x}{ - 2} = \frac{ - 70}{ - 2} }}[/tex] { Divide both sides by -2 }
[tex] \longrightarrow{ \sf{x = 35}}[/tex]
The value of x is 35°
Now, As we are asked to find the value of m [tex] \angle[/tex] ABC , replace the value of x :
[tex] \sf{m \angle \: ABC \: = (3x - 70) \degree}[/tex]
[tex] \dashrightarrow{ \sf{(3 \times 35 - 70) \degree}}[/tex]
[tex] \dashrightarrow{ \sf{(105 - 70) \degree}} [/tex]
[tex] \longrightarrow{ \boxed{ \sf{35 \degree}}}[/tex]
Therefore , m [tex] \angle[/tex] ABC = 35°
And we're done !
Hope I helped!
Best regards! :)
~TheAnimeGirl
