You can use exterior angles and the fact that sum of exterior angles of a polygon is of 360 degrees.
The measurement of angle B is given by:
Option B: [tex]108^\circ[/tex]
What is exterior angle in a polygon?
In a polygon, every pair of two adjacent sides make an angle. This is called interior angle. If you extend one of the side outwards, then the angle made outside by that extended side with another side outside of the polygon is called exterior angle.
Since both exterior angle and interior angle fill up a straight line, thus they are supplementary angles (one angle is 180 degree - another angle)
What is the sum of exterior angles of a polygon?
The sum of all exterior angles of a polygon is [tex]360^\circ[/tex]
A polygon is just a closed figure made up with straight line segments joined end to end.
Using the above fact, we have:
[tex]Exterior(\angle A) = 180^\circ - Interior(A) = 180^\circ - 170^\circ = 10^\circ\\Exterior(\angle B) = 180^\circ - Interior(B) = 180^\circ - x \text{\: (say)}\\Exterior(\angle C) = 180^\circ - 133^\circ = 47^\circ\\Exterior(\angle D) = 180^\circ - 102^\circ = 78^\circ \\Exterior(\angle E) = 180^\circ - 117^\circ = 63^\circ\\Exterior(\angle F) = 180^\circ - 90^\circ = 90^\circ[/tex]
Summing them,
[tex]10 + 180 - x + 47 + 78 + 63 + 90 = 360\\468 - x = 360\\x = 468 - 360 = 108^\circ[/tex]
Thus, the interior angle on B is of [tex]108^\circ[/tex]
Thus, the measurement of angle B is given by:
Option B: [tex]108^\circ[/tex]
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