Question

Solve for X. Justify your answer. B. 4 (21-12) (21 – 12) 1 45° (4x + 43) D c

Answer 1

We can find the value of x by using Exterior Angle property:

Exterior Angle:

The exterior angle of a triangle is the angle formed between one side of a triangle and the extension of its adjacent side.

So, in the given figure we hvae exterior angle : BAD

Property of Exterior Angle:

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

So, from the property :

$\angle BAD=\angle BCA+\angle CBA$

Now, substiute the given values of angle from the given figure:

$\angle BAD=145,\text{ }\angle BCA=(4x+43),\text{ }\angle CBA=(2x-12)$

thus,

$\begin{gathered} \angle BAD=\angle BCA+\angle CBA \\ 145=(4x+43)+(2x-12) \\ 145=4x+43+2x-12 \\ 145=6x+31 \\ 6x=145-31 \\ 6x=114 \\ x=\frac{114}{6} \\ x=19 \end{gathered}$

So, we get x = 19

Answer : x = 19