Two angles are supplementary with measures m∠ACB=4x° and m∠BCD=(6x+50)° . What is the measure of ∠ACB ?
Since two angles are supplementary, their measures add up to 180 degrees. Therefore, we have the equation:
m∠ACB + m∠BCD = 180°
Substituting the given values:
4x + (6x + 50) = 180
Combining like terms:
10x + 50 = 180
Subtracting 50 from both sides:
10x = 130
Dividing both sides by 10:
x = 13
Substituting the value of x back into the equation for m∠ACB:
m∠ACB = 4x = 4(13) = 52
Therefore, the measure of ∠ACB is 52 degrees.