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.