Answer:
m<DAE = 35°
m<ECB = 37°
m<EBC = 71°
Explanation:
✔️Find m<DAE
∆ADE is said to be an isosceles triangle, therefore, the base angles, <DAE and <AED are of equal measures.
Thus, m<ADE is given as 110°. Therefore,
m<DAE = ½(180 - m<ADE)
Substitute
m<DAE = ½(180 - 110)
m<DAE = ½(70)
m<DAE = 35°
✔️Find m<ECB:
We are told that segment EC bisects <DCB. This implies that <DCB is divided into two equal angles, which are <ECD and <ECB.
This means that:
m<ECD = m<ECB
Since m<ECD is given as 37°, therefore:
m<ECD = m<ECB = 37°
m<ECB = 37°
✔️Find m<EBC:
m<EBC = 180 - (m<CAB + m<ACB)
m<CAB = m<DAE = 35°
m<ACB = 2(m<ECD) = 2(37) = 74°
Plug in the values
m<EBC = 180 - (35 + 74)
m<EBC = 180 - 109
m<EBC = 71°
