Question

this question is only for genius

Answer 1

Let angle DBC be angle 3
Angle 1+ angle 3=90 degree
Angle3 +angle 2=90 degree comparing both values we get Angle 1+ Angle 3= Angle 3+ Angle 2 therefore angle 1 =angle 3

Answer 2

Hi friend!

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Let's take Angle DBC as Angle x.
Then Angle 1 + Angle x = 90° (Since ∆ABC is right-angled at B)

Now since Angle D is 90° (at both sides) the remaining two angles would add up to 90°. (angle-sum property)
So, Angle x + Angle 2 = 90°

Combining both of them, we get:
$x + Angle \: 1 = 90 = x + Angle \: 2 \\ x + Angle \: 1 = x + Angle \: 2 \\ x + Angle \: 1 - x = x + Angle \: 2 - x \\ Angle \: 1 = Angle \:2 \\ \\ Therefore, \: proved.$

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