Answer:
[tex] \huge{ \boxed{ \bold{ \tt{46 \degree}}}}[/tex]
Step-by-step explanation:
Given :
- [tex]\sf{m \angle \: A \: = \: (2x + 30)°} [/tex]
- [tex] \sf{ \: m \angle \: B \: = (7x - 3)°}[/tex]
To find :
- [tex] \sf{measure \: of \angle \: B} \: = ? [/tex]
Solution :
Remember that the sum of complementary angles is always 90°.
First, finding the value of x :
Set up an equation :
[tex] \sf{(2x + 30) + (7x - 3) = 90°}[/tex] ( Being complementary angles )
Solve for x
[tex] \sf{⇢2x + 30 + 7x - 3 = 90°}[/tex] { Remove unnecessary parentheses }
[tex] \sf{⇢9x + 30 - 3 = 90°}[/tex] { Combine like terms }
[tex] \sf{⇢9x + 27 = 90°}[/tex] { Subtract 3 from 30 }
[tex] \sf{⇢ \: 9x = 90° - 27}[/tex] { Move 27 to right hand side and change it's sign }
[tex] \sf{⇢ \: 9x = 63°}[/tex] { Subtract 27 from 90}
[tex] \sf{⇢ \: \frac{9x}{x} = \frac{63°}{9}} [/tex] { Divide both sides by 9 }
[tex] \sf{⇢ \: x = 7°}[/tex]
The value of X is 7°
Now, Replacing the value of x in order to find the value of [tex] \angle[/tex] B
[tex] \sf{(7x - 3)°}[/tex]
[tex] \sf{⇢ \: (7 \times 7 - 3)°}[/tex] { Plug the value of x }
[tex] \sf{⇢ \: (49 - 3)°}[/tex] { Multiply 7 by 7 }
[tex] \sf{⇢ \boxed{46°}}[/tex] { Subtract 3 from 49 }
The measure of [tex] \angle[/tex] B is 46°
And we're done!
Hope I helped!
Best regards! :D
~TheAnimeGirl
