Question

PLZ HELP ME FAST! Given that ∠MQL = 180° and ∠XQR = 180°, which equation could be used to solve problems involving the relationships between ∠MQR and ∠XQL?
A) (−5b + 115) = (125 − 10b)
B) (−5b + 115) + (125 − 10b) = 180
C) (−5b + 115) − (125 − 10b) = 180
D) (−5b + 115) − 180 = (125 − 10b)

Answer 1

A is true
because XQL = MQR

Answer 2

Given

∠MQL=180°

∠XQR=180°

Hence ∠MQL=∠XQR

(We know that ∠MQL is the sum of ∠MQR and ∠RQL

and ∠XQR is the sum of ∠XQM and ∠MQR)

lets plug in these in our equation

∠MQL=∠XQR

∠MQR + ∠RQL = ∠XQM + ∠MQR

We can cancel out ∠MQR

hence ∠RQL = ∠XQM

hence we can infer that the opposite angles of intersecting lines are equal

similarly

∠MQR = ∠XQL

which is

125-10b = -5b+115

Hence the right option is A)