Question

In the figure below angle ABD measures 41° what is the measure of angle ABC?

Answer 1

It's going to be 82 (A)i think .

Answer 2

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.