Answer: m∠ABC = 54° and m∠DBC= 30°
Step-by-step explanation: To find the measures of each angle, you have to make it into an equation to solve for .
In this case, the equation is (3x + 3) + (6x - 1) = 83°
First you combine like terms. In this case the 3x and the 6x have to be combined. 3x + 6x = 9x. The 3 and -1 have to be combined as well. 3 - 1 = 2.
Now you have 9x + 2 = 83°
Subtract 2 from each side and you are left with 9x = 81°.
Now divide each side by 9 and you are left with x = 9.
Now that you know the value of x, you will have to apply it to the equation for each angle.
m∠ABC = 6(9) - 9 = 53
m∠ABC = 53°
m∠DBC = 3(9) + 3 = 30
m∠DBC = 30°
In conclusion, the measure of angle ABC 53° and the measure of angle DBC is 3°.
Hoped this helped!!