6. ∠P and ∠Q are supplementary. m∠P = 5x + 3 and m∠Q = x + 3. x = ? (4 pts)
Given that ∠P and ∠Q are supplementary, we know that the sum of their measures is 180°. So, we can set up the equation:
m∠P + m∠Q = 180°
Substituting the measures of ∠P and ∠Q, we have:
(5x + 3) + (x + 3) = 180
Combining like terms:
6x + 6 = 180
Subtracting 6 from both sides:
6x = 174
Dividing both sides by 6:
x = 29
Therefore, x = 29.