Answer:
x = 26 m∠DAB = 80° m∠ADC = 100°
Step-by-step explanation:
Given,
ABCD is a parallelogram in which AB ║ DC and AD║ BC.
m∠DAB = 4x-24
m∠ADC = 2x+48
Solution,
Since ABCD is a parallelogram so sum of two consecutive angle is 180°.
[tex]m\angle DAB+m\angle ADC=180\°\\4x-24+2x+48=180\°\\6x+24=180\°\\6x=180-24\\6x=156\\x=\frac{156}{6}=26[/tex]
Now substituting the value of x we get the value of ∠DAB and ∠ADC .
[tex]m\angle DAB=4x-24=4\times26-24=104-24=80\°[/tex]
[tex]m\angle ADC=2x+48=2\times26+48=52+48=100\°[/tex]
Thus the value of x is 26 and m∠DAB is 80° and m∠ADC is 100°
