Question

Given: ∠ABC is ⊥; ∠1 and ∠3 are complementary.
Prove: ∠2 ⩭∠3

Answer 1

Given :

• ∠ABC is ⊥ or ∠ABC is 90°
• ∠1 and ∠3 are complementary.

To prove :

• ∠2 ⩭ ∠3

Solution :

As, ∠ABC = 90°, and ∠ABC = ∠ABE + ∠EBC

=> ∠ABE + ∠EBC = 90°

=> ∠1 + ∠2 = 90° - (i)

Now, we are given that ∠1 and ∠3 are complementary.

=> ∠1 + ∠3 = 90° - (ii)

Now, from equation (i) and (ii), we have :

• ∠1 + ∠2 = ∠1 + ∠3

=> ∠2 = ∠3

Hence, ∠2 ⩭∠3.

Answer 2

angle 2 is congruent to angle 3 because 1 and 2 are complementary and 1 and 3 are complementary.

Complementary angles are angles that sum up to 90°. Examples are 30 and 60 , 10 and 80 e.t.c

Since angle ABC is perpendicular, this beans ABC is 90°

therefore ;

angle 1 + angle 2 = 90°

angle 1 and 3 are complementary, this means

angle 1 + angle 3 = 90

Therefore;

angle 1 + angle 3 = angle 1 + angle 2

subtract angle 1 from both sides

angle 3 = angle 2

Therefore, angle 3 and angle 2 are congruent.