Answer:
x = 155°
Step-by-step explanation:
Given hexagon ABCDEF, you want to find the measure of interior angle E. Angles at vertices A, B, C, D, and F are specified.
Angle sum
The sum of the interior angles of an n-sided polygon is ...
angle sum = (n -2)180°
For the 6-sided polygon given, the sum of interior angles is ...
(6-2)180° = 720°
Application
The interior angle at vertex B is 360° -80° = 280°.
The interior angle at vertex D is 180° -115° = 65°.
Then the sum of interior angles is ...
A +B +C +D +E +F = 720°
85° +280° +30° +65° +x +105° = 720° . . . . . substitute known values
565° +x = 720° . . . . . . . collect terms
x = 155° . . . . . . . . . . subtract 565°
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Additional comment
The angles in the attached figure are drawn to scale.
An alternate solution might draw segment CX through vertex B so that the figure containing angle x has no reflex interior angles. Then the interior angles of pentagon ABXEF will total 540°. Known angles in that figure are A=85°, B=100°, X=95°, F=105°. Then E=x=540° -385° = 155°.
We took this approach initially, to verify that the angle sum of the given hexagon remained 720° even with the reflex interior angle at B.
