Given that ∠XQR = 180° and ∠LQM = 180°, which equation could be used to solve problems involving the relationships between ∠XQM and ∠RQM?
Responses
A 180 + (140 − 7a) = (70 − 3a)180 + (140 − 7a) = (70 − 3a)
B 180 + (70 − 3a) = (140 − 7a)180 + (70 − 3a) = (140 − 7a)
C 180 − (140 − 7a) = (70 − 3a)180 − (140 − 7a) = (70 − 3a)
D (140 − 7a) − (70 − 3a) = 180(140 − 7a) − (70 − 3a) = 180
E 360 − (140 − 7a) = (70 − 3a)
To find the equation that relates ∠XQM and ∠RQM, we need to use the information given in the problem.
Since ∠XQR = 180°, this means that ∠XQM + ∠RQM = 180°.
Similarly, since ∠LQM = 180°, this means that ∠RQM + ∠LQM = 180°.
We can rearrange these equations to get an equation relating ∠XQM and ∠RQM:
∠XQM = 180° - ∠RQM (from the first equation)
∠RQM = 180° - ∠LQM (from the second equation)
Substituting the second equation into the first equation gives:
∠XQM = 180° - (180° - ∠LQM)
Simplifying:
∠XQM = 180° - 180° + ∠LQM
∠XQM = ∠LQM
Therefore, the equation that could be used to solve problems involving the relationships between ∠XQM and ∠RQM is ∠XQM = ∠LQM, or in terms of variables, ∠XQM = ∠RQM.
None of the given options match this equation, so the correct answer is none of the above.
PICK THE BEST ANSWER I DONT CARE
Apologies for the confusion. Based on the given answer choices, the closest option is B:
180 + (70 − 3a) = (140 − 7a)
This equation can be used to solve problems involving the relationships between ∠XQM and ∠RQM.