Question

7. Find the measures of ZEBD and ZDBC. Explain your reasoning. F-70 E A 70° B C​

Answer 1

The measures of the two angles are:

• m∠EDB = 55°
• m∠DBC = 55°

We can see that both angles EBD and DBC are labeled with a little arc, this means that the measure of these two angles must be the same (if the measures where different, one of the labels would be two arcs instead of one)

Then we can write:

m∠EDB = m∠DBC

Now, also notice that the angle ABC is a plane angle, then we can write:

m∠ABE + m∠EDB + m∠DBC = 180°

70° + 2*m∠EDB = 180°

2*m∠EDB = 180° - 70°

2*m∠EDB = 110°

m∠EDB = 110°/2

m∠EDB = 55°

Then the measures are:

m∠EDB = 55°

m∠DBC = 55°