So, to do this, all you need to do is add up all the values, and then, with that number, divide by how many values are given.
150+165+165= 480
480/3= 160
A = 3,953 in²
You find the area of the whole triangle:
1/2bh = 1/2(63+31)(63+62) = 5875
Then subtract the missing rectangle:
lw = (62)(31) = 1922
5875 - 1922 = 3953 inches
Since you're multiplying inches by inches, it's inches².
we know that
The measure of the interior angle is the half-sum of the arcs comprising it and its opposite.
so
<u>Find the measure of the angle LAM</u>
m∠LAM is equal to
![\frac{1}{2}*[arc\ KJ+arc\ LM]= \frac{1}{2}*[170+80]\\\\=125\ degrees](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%2A%5Barc%5C%20KJ%2Barc%5C%20LM%5D%3D%20%5Cfrac%7B1%7D%7B2%7D%2A%5B170%2B80%5D%5C%5C%5C%5C%3D125%5C%20degrees)
<u>Find the measure of the angle MAJ</u>
we know that
m∠LAM+m∠MAJ=
° ------> by supplementary angles
m∠MAJ=![(180-125)](https://tex.z-dn.net/?f=%28180-125%29)
m∠MAJ=
°
therefore
<u>the answer is</u>
The measure of the angle MAJ is ![55\ degrees](https://tex.z-dn.net/?f=55%5C%20degrees)
Answer:
Length: 21 cm and Width: 6cm
Step-by-step explanation:
Let
be the width and
length of the rectangle. We know:
-------- eq. 1
(Perimeter of the rectangle) ------- eq. 2
Substitute equation 1 in equation 2:
![54 = 2(4y-3) + 2y\\54 = 8y - 6 + 2y\\54 + 6 = 8y + 2y\\60 = 10 y\\\\\frac{60}{10}= y\\y = 6](https://tex.z-dn.net/?f=54%20%3D%202%284y-3%29%20%2B%202y%5C%5C54%20%3D%208y%20-%206%20%2B%202y%5C%5C54%20%2B%206%20%3D%208y%20%2B%202y%5C%5C60%20%3D%2010%20y%5C%5C%5C%5C%5Cfrac%7B60%7D%7B10%7D%3D%20y%5C%5Cy%20%3D%206)
Using the value of y, we find x.
![x = 4y - 3\\x = 4(6) -3\\x= 24 - 3\\x = 21](https://tex.z-dn.net/?f=x%20%3D%204y%20-%203%5C%5Cx%20%3D%204%286%29%20-3%5C%5Cx%3D%2024%20-%203%5C%5Cx%20%3D%2021)
In this question, we have to find the complement and supplement of the given angles .
Complementary angles are those angles whose sum is 90 degree and supplementary angles are those angles whose sum is 180 degree.
So to find the complement and supplement angles, we need to subtract the given angles from pi/2 and pi respectively .
a.
![\frac{ \pi}{10} \\ complement \ angle = \frac{ \pi}{2} - \frac{ \pi}{10} \\ = \frac{4 \pi}{10} = \frac{ 2 \pi}{5} \\ Supplement \ angle = \pi - \frac{ \pi}{10} = \frac{9 \pi}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B%20%5Cpi%7D%7B10%7D%0A%5C%5C%0Acomplement%20%20%5C%20angle%20%3D%20%5Cfrac%7B%20%5Cpi%7D%7B2%7D%20-%20%5Cfrac%7B%20%5Cpi%7D%7B10%7D%20%20%20%20%20%5C%5C%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%3D%20%5Cfrac%7B4%20%5Cpi%7D%7B10%7D%20%3D%20%5Cfrac%7B%202%20%5Cpi%7D%7B5%7D%0A%5C%5C%0ASupplement%20%20%5C%20angle%20%3D%20%5Cpi%20-%20%5Cfrac%7B%20%5Cpi%7D%7B10%7D%20%3D%20%5Cfrac%7B9%20%5Cpi%7D%7B10%7D)
b.
![\frac{9 \pi}{10} \\ Complement \ angle = \frac{ \pi}{2} - \frac{9 \pi}{10} = \frac{-4 \pi}{10} = -\frac{2 \pi}{5} \\ Supplement \ angle = \pi - \frac{9 \pi}{10} = \frac{ \pi}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B9%20%5Cpi%7D%7B10%7D%0A%5C%5C%0AComplement%20%5C%20angle%20%3D%20%5Cfrac%7B%20%5Cpi%7D%7B2%7D%20-%20%5Cfrac%7B9%20%5Cpi%7D%7B10%7D%20%3D%20%5Cfrac%7B-4%20%5Cpi%7D%7B10%7D%20%3D%20-%5Cfrac%7B2%20%5Cpi%7D%7B5%7D%0A%5C%5C%0ASupplement%20%5C%20angle%20%3D%20%5Cpi%20-%20%5Cfrac%7B9%20%5Cpi%7D%7B10%7D%20%3D%20%5Cfrac%7B%20%5Cpi%7D%7B10%7D)