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# Find the measure of angle T

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Find the measure of angle T

Feb 5, 2021

#1
+1

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

Feb 5, 2021
#2
+1

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

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

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

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

Combine                                                     14x + 94o  =  360o

14x  =  266o

x  =  19o

Angle T = 19o + 37o  =  56o

.

Feb 5, 2021
#3
+1208
+2

x + 37 +7x - 9 = 180

8x = 152

x = 19

Feb 5, 2021
#4
0

This solution for 'x' assumes the opposite sides are equal or parallel   .... which is not stated. ....or that this is a cyclical quadrilateral...also not stated.

Guest Feb 5, 2021