An archaeologist is categorizing the artifacts he has discovered. two-thirds of the artifacts are shards of pottery. one-eighth of the artifacts are tools. the remaining artifacts are personal items, such as buttons, jewelry, and fragments of clothing. the archaeologist has discovered a total of 72 artifacts. how many of these are personal items?

Personal items=15

Step-by-step explanation:

We are given:

Total number of artifacts = 72.

We are told that 2/3 of total artifacts are shards of pottery.

We are also told that 1/8 of total artifacts are tools.

Now we will find out number of personal items by subtracting combined number of shards of pottery and tools from total number of artifacts.

Therefore, there are 15 personal items.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq