Find the measure of angle T

Since we do not know if the opposite sides are parallel or not  (even though they LOOK like they are...) we'll have to find the value of 'x' and then compute angle T

The interior angles summed = 360

6x +10     +     x+37     +      56      + 7x-9 = 360

14x + 94 = 360

x = 19

 

Angle T = x + 37 = 19 + 37 = 56 ^o

 

The sum of the interior angles of any polygon with n sides is (n – 2) • 180^o  

 

So in this 4-sided figure, the sum of the four interior angles is 360^o  

 

Add 'em up:    (6x + 10^o) + (x + 37^o) + (7x – 9^o) + (56^o)  =  360^o  

 

Rearrange       6x + x + 7x  +  10^o + 37^o – 9^o + 56^o     =  360^o   

 

Combine                                                     14x + 94^o  =  360^o 

 

                                                                     14x  =  266^o  

 

                                                                         x  =  19^o  

 

                                           Angle T = 19^o + 37^o  =  56^o  

_.

x + 37 +7x - 9 = 180

 

8x = 152

 

x = 19