Solve for x round to the nearest tenth.
2 answers:
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Answer:
The statements about arcs and angles that are true in the figure are;
1) ∠EFD ≅ ∠EGD
2)
3) mFD = 120°
Step-by-step explanation:
1) ∠ECD + ∠CEG + ∠CDG + ∠GDE = 360° (Sum of interior angle of a quadrilateral)
∠CEG = ∠CDG = 90° (Given)
∠GDE = 60° (Given)
∴ ∠ECD = 360° - (∠CEG + ∠CDG + ∠GDE)
∠ECD = 360° - (90° + 90° + 60°) = 120°
∠ECD = 2 × ∠EFD (Angle subtended is twice the angle subtended at the circumference)
120° = 2 × ∠EFD
∠EFD = 120°/2 = 60°
∠EFD ≅ ∠EGD
∠ECD = 120°
∠EGD = 60°
∴∠EGD ≠ ∠ECD
2) Given that arc mEF ≅ arc mFD
Therefore, ΔECF and ΔDCF are isosceles triangles having two sides (radii EC and CF in ΔECF and radii EF and CD in ΔDCF
∠ECF = mEF = mFD = ∠DCF (Given)
∴ ΔECF ≅ ΔDCF (Side Angle Side, SAS, rule of congruency)
(Corresponding Parts of Congruent Triangles are Congruent, CPCTC)
∠FED ≅ ∠FDE (base angles of isosceles triangle)
∠FED + ∠FDE + ∠EFD = 180° (sum of interior angles of a triangle)
∠FED + ∠FDE = 180° - ∠EFD = 180° - 60° = 120°
∠FED + ∠FDE = 120° = ∠FED + ∠FED (substitution)
2 × ∠FED = 120°
∠FED = 120°/2 = 60° = ∠FDE
∴ ∠FED = ∠FDE = ∠EFD = 60°
ΔEFD is an equilateral triangle as all interior angles are equal
(definition of equilateral triangle)
3) Having that ∠EFD = 60° and ∠CFE = ∠CFD (CPCTC)
Where, ∠EFD = ∠CFE + ∠CFD (Angle addition)
60° = ∠CFE + ∠CFD = ∠CFE + ∠CFE (substitution)
60° = 2 × ∠CFE
∠CFE =60°/2 = 30° = ∠CFD
(radii of the same circle)
ΔFCD is an isosceles triangle (definition)
∠CFD ≅ ∠CDF (base angles of isosceles ΔFCD)
∠CFD + ∠CDF + ∠DCF = 180°
∠DCF = 180° - (∠CFD + ∠CDF) = 180° - (30° + 30°) = 120°
mFD = ∠DCF (definition)
mFD = 120°.
Answer:
- 914.4 mm
- 0.0479594 km
Step-by-step explanation:
For units conversion, use a conversion factor ratio with the units you do want in the numerator and the units you don't want in the denominator. The numbers in the numerator and denominator give the ratio a value of 1: the numerator is equal to the denominator--just in different units.
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1. For feet to mm, you need a couple of additional conversion factors besides the ones shown:
1 foot = 12 in
1 cm = 10 mm
So, the conversion is ...
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2. The additional factor you need for this problem is ...
1 mile = 5280 feet
So, the conversion is ...
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<em>Additional comment</em>
You can use Google to do units conversion by typing "3 feet to mm" or "157 feet to km". However, the conversion factor for the latter will be more exact than the one given in this problem. Hence the Google answer to the second question will not be applicable here.