Answer: The measures of angles of Δ ADE are, m∠ ADE = m∠DAE= 34° and m∠DEA = 112°
Step-by-step explanation:
Here, AD and BE are the angle bisectors of ∠A and ∠B
Therefore, m∠BAD = m∠DAE = m∠ CAB/2 -------(1)
And, m∠ABE = m∠ EBD
Now, DE║AB
Therefore, m∠BAD = m∠ ADE ( By the alternative interior angle theorem)
⇒ m∠ CAB/2 =m ∠ ADE -----------(2)
But given, m∠ CAB - m∠ ADE = 34°
⇒ m∠ CAB - m∠ CAB/2 = 34°
⇒m∠ CAB/2 = 34⇒ m∠CAB = 68°
⇒ m∠ ADE = 68°/2 = 34° ( By equation (2) )
And, m∠DAE = 34°
Since, in Δ ADE,
m∠ ADE + m∠DAE + m∠DEA = 180°
⇒ m∠DEA = 112°
