Question

I need help with this I don’t understand it

Answer 1

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,

`:\implies\rm{16x - 55 = 5x - 13 + 90}`

`:\implies\rm{16x - 5x - 55 + 13 = 90}`

`:\implies\rm{11x - 42 = 90}`

`:\implies\rm{11x = 90 + 42}`

`:\implies\rm{11x = 132}`

`:\implies\rm{x = (132)/(11) }`

`:\implies\rm{x = 12}`

For angle <ADC = (16x - 55)°

`:\implies\rm{16* 12 - 55}`

`:\implies\rm{192 - 55}`

`:\implies\rm{137}`

For angle <ADB = (5x - 13)°

`:\implies\rm{5 * 12 - 13}`

`:\implies\rm{60 - 13}`

`:\implies\rm{47}`

• The measure of angles are 137° and 47°.

Answer 2

• ∠ADB = 47°
• ∠ADC = 137°

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°