If m∠1 = 105 and m∠4 = 115, then m∠6 =
40, 50, 60, 75

Solution:

m∠1 = 105,

Since m∠1 and m∠2 are supplementary

m∠2 = 180 - 105 = 75

Similarly,

m∠3 and m∠4 are supplementary and hence

m∠4 = 115

m∠3 = 180 - 115 = 65

Since l ∥ m

m∠2 = m∠5

And

m∠3 = m∠7

Therefore

m∠5 = 75

m∠7 = 65

We also know that

m∠5 + m∠6 + m∠7 = 180

75 + m∠6 + 65 = 180

m∠6 + 140 = 180

Hence

m∠6 = 180 - 140 = 40

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If m∠1 = 105 and m∠4 = 115, then m∠6 = 40, 50, 60, 75

Summary:

If m∠1 = 105 and m∠4 = 115, then m∠6 = 40