Question

7. In the accompanying diagram of rhombus CDEF, diagonal FD is drawn and the

mZE = 40. Find the m_CFD.
40
D

Answer 1

The measure of angle CFD is 70°

A rhombus is a quadrilateral with four equal sides. Opposite angles are equal, and diagonals bisect each other at right angles.

Therefore;

angle C = angle E = 40°

angle CFD = angle CDF

let angle CFD = x

Therefore;

x + x + 40 = 180

2x = 180 - 40

2x = 140

x = 140/2

x = 70

Therefore, the measure of angle CFD is 70°

Answer 2

m∠CFD is 70°

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 =
`(1)/(2)` m∠F

∴ m∠CFD =
`(1)/(2)` (140°)

∴ m∠CFD = 70°