Answer:
[tex] \boxed{ \bold{ \sf{x = 16}}}[/tex]
[tex] \boxed{ \bold{ \sf{m < AFD = 82}}}[/tex]
Step-by-step explanation:
[tex] \sf{5x + 18 = 3x + 50}[/tex]
( Being vertically opposite angles)
Vertically opposite angles are always equal.
Move variable to L.H.S and change it's sign
Similarly, Move constant to R.H.S and change it's sign
⇒[tex] \sf{5x - 3x = 50 - 18}[/tex]
Collect like terms
⇒[tex] \sf{2x = 50 - 18}[/tex]
Subtract 18 from 50
⇒[tex] \sf{2x = 32}[/tex]
Divide both sides of the equation by 2
⇒[tex] \sf{ \frac{2x}{2} = \frac{32}{2} }[/tex]
Calculate
⇒[tex] \sf{x = 16}[/tex]
The value of x is 16
Now, let's find value of m<AFD :
[tex] \sf{m < afd + 5x + 18 = 180}[/tex] ( sum of angle in straight line )
plug the value of x
⇒[tex] \sf{m < AFD + 5 \times 16 + 18 = 180}[/tex]
Multiply the numbers
⇒[tex] \sf{m < AFD + 80 + 18 = 180}[/tex]
Add the numbers
⇒[tex] \sf{m < AFD + 98 = 180}[/tex]
Move constant to R.H.S and change it's sign
⇒[tex] \sf{m < AFD = 180 - 98}[/tex]
Subtract 98 from 180
⇒[tex] \sf{m < AFD = 82}[/tex]
Value of m<AFD = 82
Hope I helped!
Best regards!!
