Question

Find the measure of the arc or angle indicated

Answer 1

80°.

Explanation:

1. if to points A and B with the centre of the given circle, then it will possible to calculate the angle AOB;

2. m∠OBC=90°, if m∠ABC=40°, then m∠ABO=m∠OBC-m∠ABC; ⇒ m∠ABO=90-40=50°;

3. in the triangle ABO OA=OB=radius, then m∠ABO=m∠BAO=50°, then

4. m∠AOB=180-(m∠ABO+m∠BAO) ⇒ m∠AOB=180-50*2=80°;

5. if m∠AOB=80°, then the m(arc AB)=80°.

PS. all the details are in the attachment.