Question

Given: Angle 1 and Angle 2 are complementary, and Angle 2 and Angle 3 are complementary. Prove: Angle 1 = Angle 3 Statements: Reasons 1. Angle 1 and angle 2 are complementary. 1. Given Angle 2 and angle 3 are complementary. 2. M angle 1 + m angle 2= 90 degrees 2. Definition of complementary m angle 2 + m angle 3= 90 degrees 3. ? 3. ? 4.? 4.? 5.? 5.? 6.? 6.?

Answer 1

See Explanation

Explanation:

`\because \angle 1` and
`\angle 2` are complementary.

`\therefore m\angle 1+m\angle 2=90\degree... (1)`

`\because \angle 2` and
`\angle 3` are complementary.

`\therefore m\angle 2+m\angle 3=90\degree... (2)`

From equations (1) & (2), we find:

`m\angle 1+m\angle 2=m\angle 2+m\angle 3</p><p>`

`m\angle 1+m\angle 2-m\angle 2=m\angle 3</p><p>`

`m\angle 1=m\angle 3`

Thus proved.

Answer 2

we have proven that if Angle 1 and Angle 2 are complementary, and Angle 2 and Angle 3 are complementary, then Angle 1 is equal to Angle 3.

Given:

Angle 1 and Angle 2 are complementary.

Angle 2 and Angle 3 are complementary.

Definition of complementary angles:

Angles are complementary if their sum is 90 degrees.

Apply the definition:

From 1, we know: ∠1 + ∠2 = 90°

From 1, we also know: ∠2 + ∠3 = 90°

Combining the equations:

(∠1 + ∠2) + ∠3 = 90° + 90°

Simplify the equation:

∠1 + ∠2 + ∠3 = 180°

We want to isolate ∠1 on one side.

Subtract ∠2 from both sides:

∠1 + ∠3 - ∠2 = 180° - ∠2

Apply the definition of complementary angles again:- Remember that ∠2 and ∠3 are complementary.

This means ∠2 + ∠3 = 90°

Substitute this into the equation:

∠1 + 90° - ∠2 = 180° - ∠2

Simplify:

Combine like terms:

∠1 + 90° = 180°

Subtract 90° from both sides:

∠1 = 180° - 90°

Simplify:

∠1 = 90°

Therefore, we have proven that if Angle 1 and Angle 2 are complementary, and Angle 2 and Angle 3 are complementary, then Angle 1 is equal to Angle 3.