When two angles are supplementary, they add up to a total of 180°. This means that if the angles’ central / connector ray is taken out, the outer extent of both angles shows up as a straight line.
Therefore, set up the equation so that the two supplementary angles equal 180°.
m∠A + m∠B = 180°
Now, substitute in each of the angle values as expression parameters.
(5x-19)° + (2x+10)° = 180°
Next, combine the like terms together (the constant with the constant, and the variable with the variable).
7x - 9 = 180
Add the inverse of the negative constant to both sides.
7x = 189
Divide both sides by 7 to get the x-variable to be by itself on one side.
x = 27
With the end goal of finding the measurement of angle B, the newfound x-value now needs to be plugged into the m∠B expression.
m∠B = (2x+10)°
Since x = 27 has been found by the supplementary angles theorem step above, the value of 27 can be directly substituted into x.
m∠B = (2 • 27 + 10)°
Then, multiply per appropriate order of operations.
m∠B = (54 + 10)°
Finally, add to reach the conclusive solution towards the measurement of angle B.
m∠B = 64°
