Answer:
x = 15
Angle ABC = 57°
Step-by-step explanation:
Hi there!
We're given:
⇒ ABD is a straight line
⇒ Angle ABC = 5x-18 degrees
⇒ Angle DBC = 8x+3 degrees
ABD is a straight line, meaning it measures an angle of 180 degrees.
Angles ABC and DBC create line ABD, so therefore, their sum is equal to 180 degrees:
[tex](5x-18)+(8x+3)=180[/tex]
Open the parentheses:
[tex]5x-18+8x+3=180[/tex]
Combine like terms:
[tex]13x-15=180\\13x=195[/tex]
Divide both sides by 13 to isolate x:
[tex]x=15[/tex]
Therefore, x = 15.
To find angle ABC, replace x with 15 in 5x-18:
[tex]5x-18\\=5(15)-18\\=75-18\\=57[/tex]
Therefore, the measure of angle ABC is 57 degrees.
I hope this helps!
