Question

Given ABD= 70° CBD= 5x+13° ABC= 3x+33° find ABC

Answer 1

In the given figure:

Angle ABD is the sum of Angle ABC and Angle CBD

i.e.

$\angle ABD=\angle ABC+\angle CBD$

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:

$\begin{gathered} \angle ABD=\angle ABC+\angle CBD \\ 70=(3x+33)+(5x+13) \\ 70=3x+33+5x+13 \\ 70=3x=5x+33+13 \\ 70=8x+46 \\ 8x=70-46 \\ 8x=24 \\ x=\frac{24}{8} \\ x=3 \end{gathered}$

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