Answer:
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]