Question

If BD bisects angle ABC, measure of DBC = 79 degrees, and measure of angle ABC= 9x-4, find the value of x.

Answer 1

Answer:  18

Step-by-step explanation:

Given :  BD bisects angle ABC, measure of DBC = 79 degrees  ---(1), and measure of angle ABC= 9x-4.   (3)

We know that if a line bisects an angle then it means that it is dividing the angle into two equal parts.

So from the given question, we have

$\angle{DBC}=\angle{DBA}=\dfrac{\angle{ABC}}{2}$         (2)

From (1) and (2), we have

$\dfrac{\angle{ABC}}{2}=79^{\circ}$

i.e. ${\angle{ABC}=2\times79=158^{\circ}$

From (3), we have

$9x-4=158\\\\\Rightarrow\ 9x=162\\\\\Rightarrow\ x=\dfrac{162}{9}=18$

Hence, the value of x = 18.

Answer 2

The value of x is: 18.

A diagram illustrating the given problem is attached below.

Given:

$m\angle ABC = 9x-4\\m\angle DBC = 79$

Thus:

Since BD bisects angle ABC, therefore:

$2(m \angle DBC) = m\angle ABC$ (angle bisector)

Plug in the values and solve for x

$2(79) = 9x-4\\158 = 9x -4\\158 + 4=9x-4+4\\162 = 9x$(Addition Property of equality)

$\frac{162}{9} =\frac{9x}{9}\\18 = x\\x = 18$

Therefore, the value of x is 18.

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