What is the measure of ∠B?

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Question:

What is the measure of ∠B?

81218523a24029b0360de9e210daa7bb

Answer:

You can use exterior angles and the fact that sum of exterior angles of a polygon is of 360 degrees.

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The measurement of angle B is given by:

Option B: ?f=108%5E%5Ccirc

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)

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What is the sum of exterior angles of  a polygon?

The sum of all exterior angles of a polygon is ?f=360%5E%5Ccirc

A polygon is just a closed figure made up with straight line segments joined end to end.

Using the above fact, we have:

?f=Exterior(%5Cangle%20A)%20%3D%20180%5E%5Ccirc%20 %20Interior(A)%20%3D%20180%5E%5Ccirc%20 %20170%5E%5Ccirc%20%3D%2010%5E%5Ccirc%5C%5CExterior(%5Cangle%20B)%20%3D%20180%5E%5Ccirc%20 %20Interior(B)%20%3D%20180%5E%5Ccirc%20 %20x%20%5Ctext%7B%5C%3A%20(say)%7D%5C%5CExterior(%5Cangle%20C)%20%3D%20180%5E%5Ccirc%20 %20133%5E%5Ccirc%20%3D%2047%5E%5Ccirc%5C%5CExterior(%5Cangle%20D)%20%3D%20180%5E%5Ccirc%20 %20102%5E%5Ccirc%20%3D%2078%5E%5Ccirc%20%5C%5CExterior(%5Cangle%20E)%20%3D%20180%5E%5Ccirc%20 %20117%5E%5Ccirc%20%3D%2063%5E%5Ccirc%5C%5CExterior(%5Cangle%20F)%20%3D%20180%5E%5Ccirc%20 %2090%5E%5Ccirc%20%3D%2090%5E%5Ccirc

Summing them,

?f=10%20%2B%20180%20 %20x%20%2B%2047%20%2B%2078%20%2B%2063%20%2B%2090%20%3D%20360%5C%5C468%20 %20x%20%3D%20360%5C%5Cx%20%3D%20468%20 %20360%20%3D%20108%5E%5Ccirc

Thus, the interior angle on B is of ?f=108%5E%5Ccirc

Thus, the measurement of angle B is given by:

Learn more about angles of polygon here:

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