What is the value of b?
80
100
75
90

The measure of ∠b is 80°

Step-by-step 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

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