Answer:
- x = 44 1/3°
- 4x = 177 1/3°
- 2x = 88 2/3°
Step-by-step explanation:
The angle sum theorem tells you the sum of angles of a triangle is 180°. Angles of a linear pair are supplementary, so total 180°. These facts can be used to write a relation that can be solved for x.
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interior angles
The interior angle at the right end of the line is the supplement of 4x:
180° -4x
The interior angle at the left end of the line is the supplement of 2x:
180° -2x
angle sum
86° +(180° -4x) +(180° -2x) = 180°
Then the solution to the triangle is ...
266° = 6x . . . . . . . . . add 6x-180°
x = 266°/6 = 44 1/3° . . . . . divide by 6
- exterior angle 4x = 177 1/3°
- exterior angle 2x = 88 2/3°
- interior left side angle 180° -88 2/3° = 91 1/3°
- interior right side angle: 180° -177 1/3° = 2 2/3°
