Answer:
x = 22.5°
Step-by-step explanation:
m∠DEA = 2x
DE || AB
m∠EAB = 2x - by Alternate Interior Angles
Exterior angle = 6x, which equals 2x + 4x
m∠BEA = 4x
Exterior Angle 4x = 2x + 2x
m∠B = 2x
2x + 4x + 2x = 180°
8x = 180°
x = 22.5°
Exterior Angles of a Triangle:
An exterior angle of a triangle is equal to the two REMOTE angles inside the triangle.
In this example, we know that 6x has remote angles of ∠EAB and ∠BEA
We found out that m∠EAB = 2x, so m∠BEA must equal 6x - 2x or 4x
Sum of angles in a Triangle:
The sum of all angles in a triangle is equal to 180°.
In this example, we found all the angles, 2x, 4x, 2x. We added all of those values to equal 8x
Since the sum of all angles = 180°:
8x = 180°
x = 180°/8
x = 22.5°
-Chetan K
