Answer:
Angle Reason
m∠ECD = 140 Given
m∠ECB = 40 Supplementary angles
m∠EBC = 70 Isosceles triangle
m∠ABE = 110 Supplementary angles
Step-by-step explanation:
Angle ECB and CED are supplementary because they form a straight line and their sum is 180 degrees. So, we can calculate the measure of ∠ECB as
m∠ECB = 180 - 140
m∠ECB = 40
Then, the interior sum of the angles of a triangle is equal to 180 degrees, so
m∠ECB + m∠EBC + m∠BEC = 180
40 + m∠EBC + m∠BEC = 180
However, m∠EBC = m∠BEC because triangle ABC is an isosceles triangle where 2 sides have the same length BC and EC. So, we can find m∠EBC as follows
40 + m∠EBC + m∠EBC = 180
40 + 2m∠EBC = 180
40 + 2m∠EBC - 40 = 180 - 40
2m∠EBC = 140
m∠EBC = 140/2
m∠EBC = 70
Then, the measure of ∠ABE is equal to
∠ABE = 180 - m∠EBC
∠ABE = 180 - 70
∠ABE = 110
Therefore, we can answer it as follows
Angle Reason
m∠ECD = 140 Given
m∠ECB = 40 Supplementary angles
m∠EBC = 70 Isosceles triangle
m∠ABE = 110 Supplementary angles