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Answer:
- m∠ADB = 108°
- m∠DCB = 72°
- m∠DBC = 36°
Step-by-step explanation:
The base angles of each isosceles triangle are congruent. So ∠ABD = ∠BAD = 36°. The exterior angle BDC is the sum of the remote interior angles BAD and ABD, so is 36°+36° = 72°. Angle DCB is congruent to that, so is 72°.
Angle BDA is the supplement of angle BDC, so is ...
∠BDA = 180° -72° = 108°
Angle DBC can be computed a couple of ways. One is to make use of the relationship to exterior angle BDA:
∠DCB +∠DBC = ∠BDA
∠DBC = 108° -72° = 36°
In summary, ...
- m∠ADB = 108°
- m∠DCB = 72°
- m∠DBC = 36°
