Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.


I need help with this I don’t understand it

I Need Help With This I Dont Understand It class=

Sagot :

sqdancefan

Answer:

  • ∠ADB = 47°
  • ∠ADC = 137°

Step-by-step explanation:

The angle addition theorem tells you an angle is the sum of its parts:

  ∠ADC = ∠ADB +∠BDC

Angle BDC is marked as a right angle, so has a measure of 90°. Filling known values into the above equation gives ...

  (16x -55)° = (5x -13)° +90°

  11x = 132 . . . . . . . . . divide by °, add 55-5x

  x = 12 . . . . . . . . . . divide by 11

Then the measures of the angles are ...

  ∠ADB = (5x -13)° = (5(12) -13)° = 47°

  ∠ADC = (16x -55)° = (16(12) -55)° = 137° . . . . . . same as 47° +90°

Here <BDC is a right angled triangle i.e (90°) and rest of the two angles are <ADC and <ADB.

Here,

<ADC = (16x - 55)°

<ADB = (5x - 13)°

<BDC = 90°

Now by applying the addition theorem property of triangle we get,

[tex]:\implies\rm{16x - 55 = 5x - 13 + 90}[/tex]

[tex]:\implies\rm{16x - 5x - 55 + 13 = 90}[/tex]

[tex]:\implies\rm{11x - 42 = 90}[/tex]

[tex]:\implies\rm{11x = 90 + 42}[/tex]

[tex]:\implies\rm{11x = 132}[/tex]

[tex]:\implies\rm{x = \frac{132}{11} }[/tex]

[tex]:\implies\rm{x = 12}[/tex]

For angle <ADC = (16x - 55)°

[tex]:\implies\rm{16\times 12 - 55}[/tex]

[tex]:\implies\rm{192 - 55}[/tex]

[tex]:\implies\rm{137}[/tex]

For angle <ADB = (5x - 13)°

[tex]:\implies\rm{5 \times 12 - 13}[/tex]

[tex]:\implies\rm{60 - 13}[/tex]

[tex]:\implies\rm{47}[/tex]

  • The measure of angles are 137° and 47°.
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.