Given parallelogram ABCD, m\angle A=5x+18 and m\angle B=3x-6 find find m\ C
1 answer:
Answer:
57
Step-by-step explanation:
Firstly, we will need to calculate what x is.
To calculate this, the important property of the parallelogram to use is that adjacent angles are supplementary.
This means A and B are supplementary while B and C are also supplementary
what we are trying to say is that they add up to be 180
Thus,
5x + 18 + 3x -6 = 180
8x +12 = 180
8x = 180-12
8x = 168
x = 168/8
x = 21
Thus, the measure of angle B is 3x-6 = 3(21) -6 = 63-6 = 57
Now, another important property of parallelograms is that opposite angles are equal. This means that angle B= C = 57
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Answer:
(t, t -1, t)
Step-by-step explanation:
You have three unknowns but only 2 equations, so you can't really SOLVE this...you can get a solution with a variable still in it (I forget what this is called. I think it refers to infinite many solutions). Here's how it works:
Set up your matrix:
You want to change the number in position 21 (the 2 in the scond row) to a 0 so you have y and z left. Do this by multiplying the top row by -2 then adding it to the second row to get that 2 to become a 0. Multiplying in a -2 to the top row gives you:
Then add, keeping the first row the same and changing the second to reflect the addition:
The second equation is this now:
3y - 3z = -3. Solving for y gives you y = z - 1. Let's let z = t (some random real number that will make the system true. Any number will work. I'll show you at the end. Just bear with me...)
lf z = t, and if y = z - 1, then y = t - 1. So far we have that y = t - 1 and z = t. Now we solve for x:
From the first equation in the original system,
x - 2y + z = 2. Subbing in t - 1 for y and t for z:
x - 2(t - 1) + t = 2. Simplify to get
x - 2t + 2 + t = 2 and x - t = 0, and x = t. So the solution set is (t, t - 1, t). Picking a random value for t of, let's say 2, sub that in and make sure it works. If:
x - 2y + z = 2, then t - 2(t - 1) + t = 2 becomes t - 2t + 2 + t = 2, and with t = 2, 2 - 2(2) + 2 + 2 = 2. Check it: 2 - 4 + 4 = 2 and 2 = 2. You could pick any value for t and it will work.