Two angles are supplementary with measures angle ACB=4x° and angle BCD=(6x+50)°. What is the measure of angle ACB?
Since the two angles are supplementary, their measures add up to 180°. So we have the equation:
angle ACB + angle BCD = 180°
Substituting the given measures into the equation:
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 original equation:
angle ACB = 4x = 4(13) = 52
So the measure of angle ACB is 52°.