Final answer:
To find the measure of angle ADC in a rhombus given the measures of angles ADB and CDB, we use the angle sum theorem. The angles in two congruent triangles formed by the diagonal BD are added and set equal to 180 degrees. By solving for x, we can find the measure of angle ADC.
Step-by-step explanation:
Given that the diagonal BD divides the rhombus ABCD into two congruent triangles, we can use the angle sum theorem to find the measure of angle ADC.
According to the angle sum theorem, the angles in a triangle add up to 180 degrees. Therefore, we have: m∠ADB + m∠BDA + m∠BAD = 180°.
Since both triangles are congruent, m∠ADB = m∠CDB. Substituting the given expressions for these angles, we get: (6x - 7) + (5x + 5) + (5x + 5) = 180°. Now we can solve for x and substitute it into the expression for angle ADC to find its measure.