The value of angle x= 24 degrees and y= 66 degrees.
As we are given two angles of a triangle as 70 degrees and 74 degrees.
We know that the sum of all the angles of a triangle is equal to 180 degrees.
Let the third angle of the big triangle is a. We can find it as follows:-
70+74+a=180
a= 180-144
a= 36 degrees .
Now, as we know that the sum of all the angles on a straight line= 180 degrees. We can find angle y as follows:-
36+78+y=180
y= 180-114
y= 66 degrees .
Now, as we know the smaller triangle has an angle of 90 degrees, angle y we have found = 66 degrees, we can find the angle x as follows:-
90+66+x=180
x= 180-156
x= 24 degrees .