Answer:
To prove A + B + C+D+E = 180°, we can use the properties of angles in a triangle and the fact that the sum of angles in a triangle is always 180°. 1. Start by considering triangle ABC.
The sum of angles in a triangle is 180°, so we have: LA + B + C = 1804° (1) 2.
Now, let's focus on triangle BCD.
Again, the sum of angles in a triangle is 180°, so we can write: LB+C+D = 180° (2) 3.
Looking at triangle CDE, we apply
the same principle: ZC+D+ZE = 1804° (3) 4.
Combining equations (1), (2), and (3), we get:
LA + B + C + D + ∠E = 1804° 5. Simplifying the equation, we have: A+B+C+D+E = 1804 Therefore, we have proven that A + B+C+D+E = 180°. It's important to note that this proof relies on the assumption that the figure is a triangle, and the angles A, B, C, D, and E are the angles within thattriangle. If the figure is not a triangle or if the angles are not associated with a triangle, this proof would not be valid.
