In circle o, and are diameters. the measure of arc ab is 55° and the measure of arc cd is 25°. circle o is shown. line segments a d and b e are diameters. line segments o f and o c are radii. what is the measure of arc e a c? 100° 125° 235° 280°

m arc EAC=280°

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc BC

we know that

m arc EAC=m arc EAB+m arc BC ----> equation A

we have

m arc EAB=180° ----> because the line segment BE is a diameter

m arc AB+m arc BC+m arc CD=180° ----> because the line segment AB is a diameter

substitute the given values and solve for m arc BC

55°+m arc BC+25°=180°

80°+m arc BC=180°

m arc BC=180°-80°=100°

step 2

Find the measure of arc EAC

m arc EAC=m arc EAB+m arc BC ----> equation A

we have

m arc EAB=180°

m arc BC=100°

substitute

m arc EAC=180°+100°=280°

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

1,918

step-by-step explanation: