PLZ HELP ME FAST! Given that ∠MQL = 180° and ∠XQR = 180°, which equation could be used to solve problems involving the relations
hips 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)
2 answers:
A is true
because XQL = MQR
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)
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