To solve the problem, we need to apply the rule
The opposite angles of a parallelogram are equal
The adjacent angles of a parallelogram are supplementary
Hence, we can write:
[tex]12x\text{ -11 = 10x + 7}[/tex]
Solving for x:
[tex]\begin{gathered} Collect\text{ like terms} \\ 12x\text{ - 10x = 7 + 11} \\ 2x\text{ = 18} \\ Divide\text{ both sides by 2} \\ \frac{2x}{2}\text{ =}\frac{18}{2} \\ x\text{ = 9} \end{gathered}[/tex]
Substitute the value of x into the expression for Q
[tex]\begin{gathered} \angle Q\text{ = 12x - 11} \\ =\text{ 12 }\times\text{ 9 - 11} \\ =\text{ 97}^0 \end{gathered}[/tex]
Solving for angle P
[tex]\begin{gathered} \angle Q\text{ + }\angle P\text{ = 180} \\ \angle P\text{ = 180 - }\angle Q \\ \angle P\text{ = 180 - 97} \\ =\text{ 83}^0 \end{gathered}[/tex]
Answer summary
[tex]\begin{gathered} m\angle\text{ Q = 97}^0 \\ m\angle P\text{ = 83}^0 \end{gathered}[/tex]
