Answer:
(i) m∠BCD = 68°
(ii) m∠DAE = 22°
Step-by-step explanation:
In a rhombus, opposite angles are equal, opposite sides are parallel and all four sides are equal
(i) Find m ∠BCD
All sides are equal
Therefore in Δ ABD is isosceles (AB = AD)
m ∠BAD = m ∠DBA = 68°
Opposite angles are equal. Therefore m∠BCD = m ∠BAD = 68°
Answer: m ∠BCD = 68°
(ii) Find m∠DAE
In triangle ADB we have angles BAD, DBA. ADB
The sum of these angles is 180°
m∠BAD + m∠DBA + m∠ADB = 180°
But m ∠BAD = m∠DBA = 68°
Therefore 68 + 68 + m∠ ADB = 180
m∠ADB = 180 - 68 - 68 = 44°
Angles ADB and ADE are a linear pair of angles so their sum must equal 180°
m∠ADB + m∠ADE = 180°
44° + m∠ADE = 180°
m∠ADE = 180° - 44° = 136°
In ∠ADE, the three angles must add up to 180°
m∠DAE + m∠AED + m∠ADE = 180
We have m∠DAE = m∠AED since triangle is isosceles (AD = DE) and DAE = 136°
So the above expression becomes
m∠DAE + m∠DAE + 136 = 180
2m∠DAE + 136° = 180°
2m∠DAE = 180° - 136° = 44°
m∠DAE = 44°/2 = 22°
Answer m∠DAE = 22°
