Given that ∠XQR = 180° and ∠LQM = 180°, which equation could be used to solve problems involving the relationships between ∠XQM and ∠RQM?
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)
B 180 + (70 − 3a) = (140 − 7a)180 + (70 − 3a) = (140 − 7a)
how did you get this
In the problem, we are given that ∠XQR = 180° and ∠LQM = 180°. This means that the sum of angles in a triangle is 180°.
In triangle QXM, we have ∠XQM + ∠MQX + ∠QXM = 180°.
Substitute the given angles into this equation:
∠XQM + 70 + 70 = 180
∠XQM + 140 = 180
∠XQM = 180 - 140
∠XQM = 40
In triangle RQM, we have ∠RQM + ∠MQR + ∠QRM = 180°.
Substitute the given angles into this equation:
∠RQM + 140 + 40 = 180
∠RQM + 180 = 180
∠RQM = 180 - 180
∠RQM = 0
Since one of the angles is 0, it seems that there is a mistake in the calculation as the sum of the angles in a triangle should be 180. Let's verify the equations:
180 + (70 − 3a) = (140 − 7a)
This equation seems to be incorrect as it does not account for the angles ∠XQM and ∠RQM.
Let's recheck the other equations.
By verifying equation B:
180 + (70 − 3a) = (140 − 7a)
Substitute the values:
180 + (70 - 3*0) = (140 - 7*0)
180 + 70 = 140
250 ≠ 140
So, in this case, B is not the correct equation to solve problems involving the relationships between ∠XQM and ∠RQM.
This will require a different equation for solving the relationship between ∠XQM and ∠RQM.