If bd bisects angle abc, measure of dbc = 79 degrees, and measure of angle abc= 9x-4, find the value of x.

The value of x is: 18.

A diagram illustrating the given problem is attached below.

Given:

Thus:

Since BD bisects angle ABC, therefore:

(angle bisector)

Plug in the values and solve for x

(Addition Property of equality)

Therefore, the value of x is 18.

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 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

        (2)

From (1) and (2), we have

i.e.

From (3), we have

Hence, the value of x = 18.

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step-by-step explanation: