Respuesta :

sqdancefan

9514 1404 393

Answer:

  m∠ADC = 86°

Step-by-step explanation:

The sum of angles making a straight angle is 180°, so we have ...

  (6x +52)° +(9x +23)° = 180°

  15x = 105 . . . . . subtract 75°, collect terms, divide by °

  x = 7 . . . . . . . . . divide by 15

m∠ADC = (9·7 +23)°

m∠ADC = 86°

∠ADC = 104°

Here given that ,

  • Line BDA is a straight line
  • Angles on the line BDA are ∠BDC & ∠ADC

As we know that , sum of angles on a straight line is always equal to 180° . So ,

=> ( 6x + 52 ) ° + ( 9x + 23 ) ° = 180°

=> 15x + 75° = 180°

=> 15x = 180° - 75°

=> 15x = 105°

=> x = 105°/15

=> x = 7°

Now , by the given information , we need to find the value of ∠ADC

  • ∠ADC = ( 9x + 23 ) °

Now substituting the value of x ,

⇒ ∠ADC = 9x + 23

⇒ ∠ADC = 9 ( 7 ) + 23

⇒ ∠ADC = 63 + 23

⇒ ∠ADC = 86°

Otras preguntas