Given are the two triangles ΔADC and ΔABC.
Given are the angles, ∡DAC = 32° and ∡DCA = 41°.
In triangle ΔADC, ∡ADC + ∡DAC + ∡DCA = 180°
∡ADC + 32° + 41° = 180°
∡ADC + 73° = 180°
∡ADC = 180° - 73°
∡ADC = 107°
Now Comparing two triangles ΔADC and ΔABC;
1. AD = AB (given in the diagram)
2. DC = BC (given in the diagram)
3. AC = AC (reflexive property)
⇒ ΔADC ≡ ΔABC (Side-Side-Side congruence)
⇒ ∡ADC = ∡ABC (CPCTC: corresponding parts of congruent triangles are congruent)
∵ ∡ADC = 107° (from triangle ΔADC)
∴ ∡ABC = 107° is the final answer.