Answer:
Option A
[tex]m\angle LQR=126^o[/tex]
Step-by-step explanation:
step 1
Find the value of b
we know that
[tex]m\angle MQR=m\angle LQX[/tex] ----> by vertical angles
substitute the given values
[tex](-3b+63)^o=(90-12b)^o[/tex]
solve for b
[tex]12b-3b=90-63\\9b=27\\b=3[/tex]
step 2
Find the measure of angle LQR
we know that
[tex]m\angle LQR+m\angle MQR=180^o[/tex] ---> by supplementary angles (form a linear pair)
[tex]m\angle MQR=(-3b+63)^o[/tex]
substitute the value of b
[tex]m\angle MQR=(-3(3)+63)=54^o[/tex]
substitute in the expression above
[tex]m\angle LQR+54^o=180^o[/tex]
[tex]m\angle LQR=180^o-54^o=126^o[/tex]
