When 43,55 and 67 are divided by a certain number, the remainder is 7 in each case. Find the number?
1 answer:
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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°