Answer: [tex]x=20[/tex]
Step-by-step explanation:
The complete exercise is: " Two angles are complementary. The measure of ∠ABC is [tex]x\°[/tex] and the measure of ∠DBC is [tex](3x + 10)\°[/tex]. What is the value of x?"
By definition, Complementary angles are those angles whose sum is 90 degrees.
In this case, knowing that the angle ∠ABC and the angle ∠DBC are Complementary angles, you can write the following equation:
[tex]\angle ABC+\angle DBC=90[/tex]
According to the data given in the exercise:
[tex]\angle ABC=x\\\\\angle DBC=3x + 10[/tex]
Knowing this, you must substitute into the equation written before:
[tex]x+3x + 10=90[/tex]
And finally you must solve for "x" in order to find its value.
This is:
[tex]x+3x + 10=90\\\\4x=90-10\\\\x=\frac{80}{4}\\\\x=20[/tex]
