Answer:
x = 87
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the opposite interior angles.
Label the angles left and right of the right angle as "a" and "b". Then we have ...
a + b + 90 = 180
b = 90 - a . . . . subtract (90+a)
And we have a relation with the left exterior angle:
72 + a = 138
a = 138 -72 = 66 . . . . subtract 72
__
b = 90 -66 = 24 . . . . from above
And another relation with the right exterior angle:
(180 -x) +b = 117 . . . . . . the interior angle with "b" is the supplement of x
204 -x = 117 . . . . . . . . . substitute 24 for b
204 -117 = x = 87 . . . . add x-117
The measure of the angle marked x° is 87°.
