Question

In quadrilateral ABCD, the sides BC and AD are congruent. The diagonal AC is the bisector of the angle BAD=160 degrees, thats is 8 times greater than angle ACB. Find the measure of angle ADC

pls help

Answer 1

Answer: $50^{\circ}$

Step-by-step explanation:

$m\angle CAB=m\angle CAD=80^{\circ}$ (angle bisector)

$m\angle ACB=20^{\circ}$ (one-eighth of $\angle BAD$)

$m\angle ABC=80^{\circ}$ (sum of angles in a triangle)

$\overline{AC} \cong \overline{BC}$ (converse of base angles theorem)

$m\angle ADC=50^{\circ}$ (base angles theorem)