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Given ∠DBC = 80° in triangle ABC, we can find ∠DAB using the fact that they are supplementary angles (sum to 180°).

Therefore, ∠DAB = 180° - ∠DBC = 180° - 80° = 100°.

From the diagram, we see that:

∠DAB and ∠DBC are supplementary angles (they add up to 180 degrees) because they are on opposite sides of the straight line BC.

We are given that the measure of ∠DBC is 80 degrees.

Therefore, to find the measure of ∠DAB, we can use the following equation:

m∠DAB + m∠DBC = 180°

Substituting the known value:

m∠DAB + 80° = 180°

Solving for m∠DAB:

m∠DAB = 180° - 80°

m∠DAB = 100°

Therefore, the measure of ∠DAB is 100 degrees.

we could have used the fact that ∠DAB and ∠BAC are exterior angles of triangle ABC. Exterior angles of a triangle are equal to the sum of the remote interior angles (the non-adjacent angles) of the triangle. In this case:

∠DAB = ∠BAC + ∠BCA

We are given that ∠BAC = -7+13x and ∠BCA = -6+4x. Substituting these values:

∠DAB = (-7+13x) + (-6+4x)

Combining like terms:

∠DAB = -13+17x

Since we already found that ∠DAB = 100 degrees, we can set these two equations equal to solve for x:

100° = -13+17x

Adding 13 to both sides:

113° = 17x

Dividing both sides by 17:

x = 7

Therefore, the measure of ∠DAB is 100 degrees, and the value of x is 7.

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