In the given figure:
Angle ABD is the sum of Angle ABC and Angle CBD
i.e.
[tex]\angle ABD=\angle ABC+\angle CBD[/tex]
From the given data, we have:
Angle ABD = 70
Angle CBD = 5x + 13
Angle ABC = 3x + 33
Substitute the value and simplify for the x:
[tex]\begin{gathered} \angle ABD=\angle ABC+\angle CBD \\ 70=(3x+33)+(5x+13) \\ 70=3x+33+5x+13 \\ 70=3x=5x+33+13 \\ 70=8x+46 \\ 8x=70-46 \\ 8x=24 \\ x=\frac{24}{8} \\ x=3 \end{gathered}[/tex]
x = 3
The expression for angle ABC is :
Angle ABC = 3x + 33
Substitute the value of x = 3 in the expression and simplify:
Angle ABC = 3x + 33
Angle ABC = 3(3) + 33
Angle ABC = 9 + 33
Angle ABC = 42°
m
Answer : m
