The measure of angle x is 50 degrees.
SOLUTION:
Given, the sum of the measures of angle x and angle y is 90.
Then, [tex]x+y=90 \rightarrow(1)[/tex]
The measure of angle x is 30 less than twice the measure of angle y,
Then, [tex]x = 30 \text { less than } 2\times y \rightarrow x = 2y-30 \rightarrow (2)[/tex]
We have to find the measure of angle x
So, now substitute (2) in (1)
Then, [tex](1) \rightarrow 2 y-30+y=90 \rightarrow 3 y=90+30 \rightarrow 3 y=120 \rightarrow y=40[/tex]
Then, [tex]x=2\times 40-30 \rightarrow x=80-30 \rightarrow x=50[/tex]
Therefore, the measure is 50 degrees
