In the diagram to the left ADE is an isosceles triangle. Segment EC bisects DCB. A. Find the measures of DAE, ECB, and EBC
B. Explain how you were able to find the measures of these three angles

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°