The angles in a triangle must add up to equal 180. When it gives you angle A and angle B, you add them, then subtract it from 180, which will give you the angle C.
65 + 15 = 80
180 - 80 = 100 = Angle C.
It says to list them from smallest to greatest.
<B = 15, <A = 65, <C = 100
Preston have to get some correct and some incorrect answers.
Answer:
C. 50 degrees
Step-by-step explanation:
Angle EDG is 90 degrees
x = 10
5 multiplied by 10 is 50
4 multiplied by 10 is 40
40+50=90
Answer:
Is an acute triangle
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
we have
G(7,3), H(9, 0), I(5, -1)
step 1
Find the distance GH
substitute in the formula
![d=\sqrt{(0-3)^{2}+(9-7)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%280-3%29%5E%7B2%7D%2B%289-7%29%5E%7B2%7D%7D)
![d=\sqrt{(-3)^{2}+(2)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-3%29%5E%7B2%7D%2B%282%29%5E%7B2%7D%7D)
![GH=\sqrt{13}\ units](https://tex.z-dn.net/?f=GH%3D%5Csqrt%7B13%7D%5C%20units)
step 2
Find the distance IH
substitute in the formula
![d=\sqrt{(0+1)^{2}+(9-5)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%280%2B1%29%5E%7B2%7D%2B%289-5%29%5E%7B2%7D%7D)
![d=\sqrt{(1)^{2}+(4)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%281%29%5E%7B2%7D%2B%284%29%5E%7B2%7D%7D)
![IH=\sqrt{17}\ units](https://tex.z-dn.net/?f=IH%3D%5Csqrt%7B17%7D%5C%20units)
step 3
Find the distance GI
substitute in the formula
![d=\sqrt{(-1-3)^{2}+(5-7)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-1-3%29%5E%7B2%7D%2B%285-7%29%5E%7B2%7D%7D)
![d=\sqrt{(-4)^{2}+(-2)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-4%29%5E%7B2%7D%2B%28-2%29%5E%7B2%7D%7D)
![GI=\sqrt{20}\ units](https://tex.z-dn.net/?f=GI%3D%5Csqrt%7B20%7D%5C%20units)
step 4
Verify what type of triangle is the polygon
we know that
If applying the Pythagoras Theorem
----> is a right triangle
----> is an obtuse triangle
----> is an acute triangle
where
c is the greater side
we have
![c=\sqrt{20}\ units](https://tex.z-dn.net/?f=c%3D%5Csqrt%7B20%7D%5C%20units)
![a=\sqrt{17}\ units](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B17%7D%5C%20units)
![b=\sqrt{13}\ units](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B13%7D%5C%20units)
substitute
![c^{2}= (\sqrt{20})^{2}=20](https://tex.z-dn.net/?f=c%5E%7B2%7D%3D%20%28%5Csqrt%7B20%7D%29%5E%7B2%7D%3D20)
![a^{2}+b^{2}=(\sqrt{17})^{2}+(\sqrt{13})^{2}=30](https://tex.z-dn.net/?f=a%5E%7B2%7D%2Bb%5E%7B2%7D%3D%28%5Csqrt%7B17%7D%29%5E%7B2%7D%2B%28%5Csqrt%7B13%7D%29%5E%7B2%7D%3D30)
therefore
![c^{2}< a^{2}+b^{2}](https://tex.z-dn.net/?f=c%5E%7B2%7D%3C%20a%5E%7B2%7D%2Bb%5E%7B2%7D)
Is an acute triangle