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nakeytrag
16.10.2020 •
Mathematics
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Ответ:
See Below.
Step-by-step explanation:
We want to write a paragraph proof to prove the following theorem:
If ∠N and ∠M are congruent and supplementary, then ∠N and ∠M are right angles.
Each sentence is numbered:
1) Because ∠N and ∠M are congruent, m∠M = m∠N by the definition of congruent angles.
2) Because ∠N and ∠M are supplementary, m∠M + m∠N = 180.
3) Substitute m∠M to m∠N to get m∠M + m∠M = 180, or 2m∠M=180.
4) The Division Property of Equality then yields m∠M = 90.
5) Substitute m∠N for m∠M to get m∠N = 90.
6) By the definition of right angles, ∠N and ∠M are right angles.
Ответ:
6π units
Step-by-step explanation:
Given::
Radius = 4
Angle measure of partial circle (θ) = 360° - right angle = 360° - 90° = 270°
Arc length = θ/360 × 2πr
Plug in the values
= 270/360 × 2 × π × 4
= 0.75 × 8 × π
= 6π units