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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

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Respuesta :

Medunno13

Answer: [tex]50^{\circ}[/tex]

Step-by-step explanation:

[tex]m\angle CAB=m\angle CAD=80^{\circ}[/tex] (angle bisector)

[tex]m\angle ACB=20^{\circ}[/tex] (one-eighth of [tex]\angle BAD[/tex])

[tex]m\angle ABC=80^{\circ}[/tex] (sum of angles in a triangle)

[tex]\overline{AC} \cong \overline{BC}[/tex] (converse of base angles theorem)

[tex]m\angle ADC=50^{\circ}[/tex] (base angles theorem)

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