Solution (1) :
Measure of angle ABC = (3x)°
Measure of angle CBD = (15x+18)°
Since angle ABC and angle CBD are a linear pair their sum will be equal to 180°¿
Which means :
[tex] =\tt 3x + 15x + 18 = 180[/tex]
[tex] =\tt 18x + 18 = 180[/tex]
[tex] = \tt18x = 162[/tex]
[tex] =\tt x = \frac{162}{18} [/tex]
[tex]\color{plum} \tt= x = 9[/tex]
Thus, the value of x = 9.
Solution (2) :
From that equation, we know that the value of x = 9.
Which means :
Measure of angle ABC :
[tex] =\tt 3x[/tex]
[tex] =\tt 3 \times 9[/tex]
[tex]\tt\color{plum} \: angle \: ABC = \tt27°[/tex]
Measure of angle ABC = 27°
Therefore, the measure of angle ABC = 27°
Solution (3) :
We know that x = 9
Which means :
Measure of angle CBD :
[tex] =\tt 15x + 18[/tex]
[tex] = \tt15 \times 9 + 18[/tex]
[tex] = \tt135 + 18[/tex]
[tex]\color{plum} \tt \: angle \: CBD = 153°[/tex]
Thus, angle CBD = 153°
Since the measure of angle ABC and angle CBD equals 180°[27+153=180°], we can conclude that we have found out the correct value of each angle.
Therefore, the measure of angle CBD = 153°
