Question

In the figure below, ZAPE and ZEPD are congruent. What is the arc measure of minor arc AC on circle P in degrees? 136° B C=74° D C =42°

Answer 1

To solve this problem, we will first find the measure of the missing angles. Let x be measure of the angle APE. We know that angles APE and EPD are congruent, so they have the same measure. So, the measure of angle EPD is also x.

Now, to find the value of x, we will proceed as follows:

If we add the measure of all central angles of a circle, we would get 360°. So doing this, we get

which gives us the equation

`136+x+x+42+74=360`

Adding up on the left side, we get

`2x+252=360`

Now, we subtract 252 on both sides, so we get

`2x=360\text{ -252 = 108}`

Finally, we divide both sides by 2, so we get

`x=(108)/(2)=54`

Now. we want the measure, in degrees of the arc AC. So, we should add the angles

APE, EPD and DPC.

So we get

`54+54+42=108`

so the measure of the arc AC in degrees is 108°.