Question

Find the measure for LQR.

Answer 1

Answer:

Option A

$m\angle LQR=126^o$

Step-by-step explanation:

step 1

Find the value of b

we know that

$m\angle MQR=m\angle LQX$ ----> by vertical angles

substitute the given values

$(-3b+63)^o=(90-12b)^o$

solve for b

$12b-3b=90-63\\9b=27\\b=3$

step 2

Find the measure of angle LQR

we know that

$m\angle LQR+m\angle MQR=180^o$ ---> by supplementary angles (form a linear pair)

$m\angle MQR=(-3b+63)^o$

substitute the value of b

$m\angle MQR=(-3(3)+63)=54^o$

substitute in the expression above

$m\angle LQR+54^o=180^o$

$m\angle LQR=180^o-54^o=126^o$