Question

calculator
rhombus abcd has a diagonal \\(\overline{bd}\\).
\\(m\angle adb = (4x - 12)\degree\\)
\\(m\angle cdb = (3x + 6)\degree\\)
what is the \\(m\angle adc\\)?
enter your answer in the box

Explanation:

Step1: Diagonals bisect angles in rhombus

Diagonal $\overline{BD}$ bisects $\angle ADC$, so $m\angle ADB = m\angle CDB$.

Step2: Set up equation for x

$4x - 12 = 3x + 6$
Solve: $4x - 3x = 6 + 12$ → $x = 18$.

Step3: Calculate $m\angle ADB$

Substitute $x=18$: $4(18)-12 = 72-12 = 60^\circ$.

Step4: Find $m\angle ADC$

$\angle ADC = 2 \times m\angle ADB = 2 \times 60 = 120^\circ$.

Answer:

120