Step-by-step explanation:
1. vertical opposite angles
2. corresponding angles
3. alternate interior angles
4. alternate exterior angles
5. corresponding angles
6. vertical opposite angles
7. alternate exterior angles
8. vertical opposite angles
9. corresponding angles
10. alternate exterior angles
Points J, K and M form a triangle.
In this triangle you are given the angles for JKM (50) and KJM (60)
The 3 inside angles of a triangle need to equal 180.
The third angle JMK would be 180 minus the two given angles:
JMK = 180 - 50 - 60 = 70
JMK = 70 degrees
Answer:
C) Trapezoid
Step-by-step explanation:
Given
![A = (0,0)](https://tex.z-dn.net/?f=A%20%3D%20%280%2C0%29)
![B = (4,8)](https://tex.z-dn.net/?f=B%20%3D%20%284%2C8%29)
![C = (12,8)](https://tex.z-dn.net/?f=C%20%3D%20%2812%2C8%29)
![D=(16,0)](https://tex.z-dn.net/?f=D%3D%2816%2C0%29)
Required
The possible shape
The above are 4 vertices.
Hence, the shape cannot be
(a) Triangle ---- it has 3 vertices
(b) Pentagon ---- it has 5 vertices
Calculate distance AB using distance formula
![AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2)
Where:
![A = (0,0)](https://tex.z-dn.net/?f=A%20%3D%20%280%2C0%29)
![B = (4,8)](https://tex.z-dn.net/?f=B%20%3D%20%284%2C8%29)
![AB = \sqrt{(0 - 4)^2 + (0 - 8)^2](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%280%20-%204%29%5E2%20%2B%20%280%20-%208%29%5E2)
![AB = \sqrt{( - 4)^2 + ( - 8)^2](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%28%20-%204%29%5E2%20%2B%20%28%20-%208%29%5E2)
![AB = \sqrt{16+64](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B16%2B64)
![AB = \sqrt{80](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B80)
![AB = 8.94](https://tex.z-dn.net/?f=AB%20%3D%208.94)
Calculate distance BC using distance formula
![BC = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2)
Where:
![B = (4,8)](https://tex.z-dn.net/?f=B%20%3D%20%284%2C8%29)
![C = (12,8)](https://tex.z-dn.net/?f=C%20%3D%20%2812%2C8%29)
![BC = \sqrt{(4 - 12)^2 + (8 - 8)^2](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%284%20-%2012%29%5E2%20%2B%20%288%20-%208%29%5E2)
![BC = \sqrt{(-8)^2 + (0)^2](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%28-8%29%5E2%20%2B%20%280%29%5E2)
![BC = \sqrt{64 +0](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B64%20%2B0)
![BC = \sqrt{64](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B64)
![BC = 8](https://tex.z-dn.net/?f=BC%20%3D%208)
Since
![AB \ne BC](https://tex.z-dn.net/?f=AB%20%5Cne%20BC)
<em>Then, the polygon is not a square</em>
<em></em>
<em>The last available option is (c) trapezoid</em>