Answer:
The measure of ∠b is 80°
Explanation:
Given the figure in which measure of angles are shown in attachment
∠4=110°, ∠6=90°
we have to find the measure of ∠b
In ΔAOB, by angle sum property
∠2+∠3+∠4=180°
2∠2+110°=180° ( ∠2=∠3 as AO=OB)
2∠2=70° ⇒ ∠2=35°
In ΔAOC, by angle sum property
∠1+∠5+∠6=180°
2∠1+90°=180° ( ∠1=∠5 as AO=OC)
2∠1=90° ⇒ ∠1=45°
By alternate segment theorem which states that the angle between a chord and a tangent through one of the end points of the chord is equal to the angle formed in the alternate segment.
∠b=∠1+∠2=35°+45°=80°
Hence, measure of ∠b is 80°
Option 1 is correct