Question

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Answer 1

∠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°

Answer 2

9514 1404 393

Answer:

m∠ADC = 86°

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°