Question

m∠dab = m∠□ + m∠□ exterior angle theorem
(12x + 7)° = (6x − 4)° + 65° substitution
x = 9 solve.
so, m∠dab = 12(9) + 7° or 115°.

Explanation:

Step1: Apply Exterior Angle Theorem

$m\angle DAB = m\angle ABC + m\angle BCA$

Step2: Substitute given angle values

$(12x + 7)^\circ = (6x - 4)^\circ + 65^\circ$

Step3: Solve for $x$

$12x + 7 = 6x - 4 + 65$
$12x - 6x = 61 - 7$
$6x = 54$
$x = 9$

Step4: Calculate $m\angle DAB$

$m\angle DAB = [12(9) + 7]^\circ$

Answer:

The missing angles in the theorem are $\angle ABC$ and $\angle BCA$; $x=9$, and $m\angle DAB=115^\circ$