Answer:
[tex]m\angle 1=20[/tex]
Step-by-step explanation:
Given:
m ∠BDC = 20
m arc AB = 140
m arc CD = 120
Now, let the center of the circle be at point 'O'.
From the triangle AOB,
OA = OB (Radius of the circle)
∴ m∠ABO = m∠BAO = m ∠1
∵ m arc AB = 140
∴ m ∠AOB = 140 (Arc measure equals the angle subtended by the arc at the center)
Now, sum of all angles of a triangle is equal to 180. So,
[tex]m\angle AOB+m\angle ABO+m\angle BAO=180\\140+m\angle 1+m\angle 1=180\\2(m\angle 1)=180-140\\2(m\angle 1)=40\\m\angle 1=\frac{40}{2}=20[/tex]
Therefore, the measure of angle 1 is 20. So, the last option is correct.
