Question

If mZBDC = 20, m arc AB = 140, and marc CD = 120, find m21.

Answer 1

Answer:

$m\angle 1=20$

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,

$m\angle AOB+m\angle ABO+m\angle BAO=180\\140+m\angle 1+m\angle 1=180\\2(m\angle 1)=180-140\\2(m\angle 1)=40\\m\angle 1=\frac{40}{2}=20$

Therefore, the measure of angle 1 is 20. So, the last option is correct.