Final answer:
To find the measure of ∠ADM, use the properties of triangles and angle bisectors in △AMD. Set up equations to find the value of X and substitute it back to find the measure of ∠ADM.
Step-by-step explanation:
To find the measure of ∠ADM, we need to use the properties of triangles and the angles in △AMD. The incenter, C, of △AMD is the point where the angle bisectors intersect. Since C is the incenter, the angle ∠AMC is equal to half the measure of ∠AMD, and the angle ∠DMC is also equal to half the measure of ∠ADM.
Given that m∠AMC = (3X + 6)° and m∠DMC = (8X − 49)°, we can set up equations to find the value of X. Add the two equations and set it equal to 180° since the angles of a triangle add up to 180°. Solve for X, and then substitute it back into the equation for m∠AMC or m∠DMC to find the measure of ∠ADM.
Finally, simplify m∠ADM to get the numerical value of the angle.