Answer:
if two angles of a triangle are complementary find the number of degrees in the third angle of the triangle
1 answer:
Answer:
The measure of the third angle is a 90 degrees
Step-by-step explanation:
Let
A and B ----> two complementary angles in a triangle
C ---> the measure of the third angle in a triangle
we know that
If two angles are complementary, then their sum is equal to 90 degrees
so
---> equation A
Remember that
The sum of the interior angles in any triangle must be equal to 180 degrees
so
----> equation B
substitute equation A in equation B
solve for C
subtract 90 degrees both sides
therefore
we have a right triangle
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Answer:
The number of candies in the sixth jar is 42.
Step-by-step explanation:
Assume that there are <em>x</em> number of candies in each of the six jars.
⇒ After Alice moves half of the candies from the first jar to the second jar, the number of candies in the second jar is:
⇒ After Boris moves half of the candies from the second jar to the third jar, the number of candies in the third jar is:
⇒ After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the fourth jar is:
⇒ After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fifth jar is:
⇒ After Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the sixth jar is:
Now, it is provided that at the end, 30 candies are in the fourth jar.
Compute the value of <em>x</em> as follows:
Compute the number of candies in the sixth jar as follows:
Thus, the number of candies in the sixth jar is 42.
Answers:
- Segment XA and segment MC
- Point N
- Points A, N and X
- Plane ANC
- No, they are not coplanar
- Ray NM and ray NX
- Ray NM and ray NC
- Three lines
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Explanation:
Problem 1
Technically there are no segments in this diagram because of the arrows that point in both directions for each line. However, you could make the argument that all you need to do is focus on two endpoints and that names a sub-segment of any given line. If this is what your teacher is going for, then two segments could be XA and MC
Something like "segment AC" isn't valid because there isn't a straight line connecting points A and C directly. So we can't pick any two points at random.
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Problem 2
Line CM and line RN intersect at point N
This point is on both lines simultaneously.
-----------------
Problem 3
Pick any three points that are on the same line. One such possible answer is Points A, N and X. They are all on the line XA.
Another possible answer would be points C, N and M.
-----------------
Problem 4
To name a plane, we can pick 3 points inside the plane that aren't collinear. One such possible answer is Plane ANC
We cannot label the plane as "plane ANX" because infinitely many planes pass through these collinear points. Think of the plane able to rotate like a propeller. So this is why we need 3 non-collinear points to uniquely define the plane.
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Problem 5
The points R, N, M and X are not in the same plane V. If we ignored point R, then the remaining points (N, M, X) are all in the same plane. However, the presence of R is what makes them not coplanar.
Think of points N, M and X being on the ground while point R is somewhere up in the air. Unfortunately the 2D diagram makes it tricky to show that R is above the plane.
So because those points are not in the same plane, we do not consider them coplanar.
-----------------
Problem 6
This is similar to problem 1. Technically there aren't any rays shown here, but we could focus on a subset of the line. Two possible answers are ray NM and ray NX
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Problem 7
Ray NM and ray NC can be glued together to form line CM. They point in completely opposite directions (eg: one points north, the other points south). Notice that rays NM and NC both start with the letter N to indicate that N is the endpoint (i.e. the part that doesn't go on forever).
Another possible answer would be ray NA and ray NX. They glue together to form line XA.
-----------------
Problem 8
There are 3 lines and they are:
- Line XA
- Line CM
- Line RN
To name a line, all we need are two points that are on the line itself. A line has a characteristic of going on forever in both directions. So that's why we have the double arrow symbol overtop the line name.
Example: