Answer: ∠ ABC=82°
Step-by-step explanation:
In the given picture, ΔABD and ΔBCD have BD as common.
In ΔABD and ΔBCD
∠C=∠A [right angle]
BD=BD [common]
CD=AD [given in the picture]
Therefore, by HL theorem ΔABD ≅ ΔBCD
⇒ ∠ABD=∠DBC=41° [corresponding parts of congruent triangles are congruent]
Now, ∠ ABC=∠ABD+∠DBC=41°+41°=82°
Hence, ∠ ABC=82°
- HL theorem says that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle then both the triangles are congruent.
