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2 years ago

HELPPP Provide the missing statements and reasons for the following proof:

Mathematics

1 answer:

agasfer [191]2 years ago

5 0

The missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:

S2: ∠2 ≅ ∠3

R2: corresponding angles

S3: m∠2 ≅ m∠3

R3: Definition of congruent angles

R5: Definition of supplementary angles

S7: m∠1 + m∠2 = 180°

S8: ∠1 is supplementary to ∠2

Given the proof to show that ∠1 is supplementary to ∠2, thus:

Since lines m and n are parallel to each other,

∠2 and ∠3 are corresponding angles, so, ∠2 ≅ ∠3 based on the corresponding angles theorem.

Since ∠1 and ∠3 form a linear pair, they are supplementary to each other.

By substitution, we would have m∠1 + m∠2 = 180°.

Therefore, we can conclude that ∠1 is supplementary to ∠2.

In summary, the missing statements and reasons in the proof showing that ∠1 is supplementary to ∠2 are:

S2: ∠2 ≅ ∠3

R2: corresponding angles

S3: m∠2 ≅ m∠3

R3: Definition of congruent angles

R5: Definition of supplementary angles

S7: m∠1 + m∠2 = 180°

S8: ∠1 is supplementary to ∠2

Learn more about supplementary angles on:

brainly.com/question/12919120

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AleksandrR [38]

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Step-by-step explanation:

The given is,

The angle of depression from the top of a building to a point on the ground is 45 degrees.

Height of the building is 280 meter.

Step: 1

Given diagram is a right angled diagram,

For right angle triangle,

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Trignometric ratio,

sin ∅ = $\frac{Opp}{Hyp}$ ....................(1)

For the above ratio take the bottom angle, that is angle of depression from the top of a building to a point on the ground is 45 degrees.

Where, Opp side = 280 meters

Hyp side = x

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Equation (1) becomes,

sin 45° = $\frac{280}{x}$

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x = $\frac{280}{0.70710678}$

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Trignometric ratio,

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Result:

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