The number of patches that Leia can cut from 32 pieces of the fabric measuring 18 cm by 10 cm will be as follows:
Number of pieces=[total area of fabric]/[area of patch]
area of fabric=18×10=180 cm²
Area of 32 patches=180×32=5760 cm²
Area of patch=45 cm²
Number of patches=5760/45=128 patches
Answer:
m∠CFD is 70°
Step-by-step explanation:
In the rhombus
- Diagonals bisect the vertex angles
- Every two adjacent angles are supplementary (their sum 180°)
Let us solve the question
∵ CDEF is a rhombus
∵ ∠E and ∠F are adjacent angles
→ By using the second property above
∴ ∠E and ∠F are supplementary
∵ The sum of the measures of the supplementary angles is 180°
∴ m∠E + m∠F = 180°
∵ m∠E = 40°
∴ 40° + m∠F = 180°
→ Subtract 40 from both sides
∵ 40 - 40 + m∠F = 180 - 40
∴ m∠F = 140°
∵ FD is a diagonal of the rhombus
→ By using the first property above
∴ FD bisects ∠F
→ That means FD divides ∠F into 2 equal angles
∴ m∠CFD = m∠EFD = m∠F
∴ m∠CFD = (140°)
∴ m∠CFD = 70°