The measure of the angle 2 in degrees is 58 degrees
How to find the measure of angle 2
sum of Angle on a straight line = 180
call the 90 degrees angle 3
Hence we have
∠1 + ∠2 + ∠3 = 180
When we fill in the values we have
90 + (3x-4) + (4x + 10) = 180
open the brackets
90 + 10 - 4 + 3x + 4x = 180
3x + 4x = 180 - 96
7x = 84
Divide through by 7
x = 12
Put the value of x in the angle 2
(4x-10)
4 * 12 + 10
= 48 + 10
= 58
Complete question
Check the attachment