Answer:
ABD = 140
DBC = 40
Step-by-step explanation:
What is shown is a <u>supplementary angle</u>. These types of angles equal 180 degrees.
So that means whatever angle measures is in the supplementary angle added together would equal 180.
The equation to solve this would be <u>(15x - 4) + (5x - 8) = 180</u>
First, I would combine like terms. The 15x and 5x can be combined together to make 20x and the -4 and -8 would be equal to -12.
The simplified equation is now <u>20x - 12 = 180.</u>
Next, we need to get rid of the 12. So we add 12 to both sides.
(20x - 12) + 12 leaves 20x by itself
180 + 12 = 192
Our equation is now <u>20x = 192</u>
Next, we have to make sure that the <em>x</em> is by itself. To do this, we have to divide each side by 20.
20x/20 leaves us with just x.
192/20 is 9.6
x is equal to 9.6
Finally, we plug in the variable's value back into the angle measures to find their value.
15(9.6) - 4 = 140
5(9.6) - 8 = 40
Therefore, ABD is <u>140</u> degrees and angle DBC is <u>40</u> degrees.
<u><em>Checking our work:</em></u>
To check if our work is right, we can add up the angle measures to see if it's equal to 180.
140 + 40 is 180, so we are correct.
I apologize if that was a lot to read, but I hope you understand!
