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Find x, where a=14 degrees and b=22 degrees. Find the measure of each angle of the polygon. Shown below.

Find x, where a=14 degrees and b=22 degrees. Find the measure of each angle of the-example-1
User Shmuels
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To answer this question, we need to remember that the sum of the interior angles of a quadrilateral is equal to 360º (in fact, we can divide a quadrilateral into two triangles, and the sum of interior angles of a triangle is equal to 180º).

Then, we have that a = 14º and b = 22º, then we can state the next equation:


(2x+14^(\circ))+(3x+22^(\circ))+2x+x=360^(\circ)

And now, we can solve the equation for x as follows:

1. Add the like terms as follows:


(2x+3x+2x+x)+14^(\circ)+22^(\circ)=360^(\circ)
8x+36^(\circ)=360^(\circ)

2. Subtract 36º from both sides of the equation:


8x+36^(\circ)-36^(\circ)=360^(\circ)-36^(\circ)\Rightarrow8x=324^(\circ)

3. Divide both sides by 8 as follows:


(8x)/(8)=(324^(\circ))/(8)\Rightarrow x=40.5^(\circ)

Therefore, the value for x = 40.5º

Then, we can find the values for the measure of angle A as follows:


m\angle A=2(40.5^(\circ))+14^(\circ)=95^(\circ)

The measure of angle B is


m\angle B=3(40.5^(\circ)_{})+22^(\circ)=143.5^(\circ)

The measure of angle C is


m\angle C=x^(\circ)=40.5^(\circ)

The measure of angle D is


m\angle D=2(40.5^(\circ))=81^(\circ)

Find x, where a=14 degrees and b=22 degrees. Find the measure of each angle of the-example-1
User Joshaber
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