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:
[tex](2x+14^{\circ})+(3x+22^{\circ})+2x+x=360^{\circ}[/tex]
And now, we can solve the equation for x as follows:
1. Add the like terms as follows:
[tex](2x+3x+2x+x)+14^{\circ}+22^{\circ}=360^{\circ}[/tex][tex]8x+36^{\circ}=360^{\circ}[/tex]
2. Subtract 36º from both sides of the equation:
[tex]8x+36^{\circ}-36^{\circ}=360^{\circ}-36^{\circ}\Rightarrow8x=324^{\circ}[/tex]
3. Divide both sides by 8 as follows:
[tex]\frac{8x}{8}=\frac{324^{\circ}}{8}\Rightarrow x=40.5^{\circ}[/tex]
Therefore, the value for x = 40.5º
Then, we can find the values for the measure of angle A as follows:
[tex]m\angle A=2(40.5^{\circ})+14^{\circ}=95^{\circ}[/tex]
The measure of angle B is
[tex]m\angle B=3(40.5^{\circ}_{})+22^{\circ}=143.5^{\circ}[/tex]
The measure of angle C is
[tex]m\angle C=x^{\circ}=40.5^{\circ}[/tex]
The measure of angle D is
[tex]m\angle D=2(40.5^{\circ})=81^{\circ}[/tex]
