Question

Prove that if the two arms of an angle are perpendicular to the two arms of another angle then the angles are either equal or supplementary.

Answer 1

$\textbf{ Hello Mate! }$

Here, /_B is 90° and /_D is 90°

As two arms are perpendicular so AB || CD. Similarly AD || BC

Now, in parallel lines the sum of interior adjacent angles is 180°. Here, all lines are transversal.

Hence proved that sum of adjacent angles is 180°

/_B + /_C = 180°

90° + /_C = 180°

/_C = 90°

Similarly, /_A + /_D = 180°

/_D = 90°

$\boxed{ Angles A=B=C=D=90° }$

Hence Proved that all angles are of 90°

Have great future ahead!

$\textbf{ Happy Independence Day }$

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Answer 2

Answer:

Let AB perpendicular to BE and AD to DE.

Now, we know that in traingle ABC and CDE  

Angle ABC = angle CDE = 90 degrees   { given }

Angle ACB = angle DCE { opposite angles are equal}

=> traingle ABC and CDE are similar  

=> angle BAC = angle CED

 

By the property of similar triangles , we can say that ,

they both are acute angles forming a supplementary angles .

Hence proved .