Explanation:
a)=
y = 70 + 41 (exterior angle is equal to sum of its opposite interior angles)
so, y = 111°
Now,
y = x + 58° ((exterior angle is equal to sum of its opposite interior angles)
or. 111° - 58° = x
so, x = 53°
b)=
x = 180° - 127° (linear pair of x is corresponding to 127)
so, x = 53°
Now,
y = 83° (y is vertically opposite to angle that is corresponding to 83)
c)= x = 47° (alternate angles)
y = 47 + 32 (exterior angle is equal to sum of its opposite interior angles)
so, y = 79°
d)= other angle = 180-45-45 = 90
Using the formula:-
sinA/a = sinB/b = sinC/c
or, sin45/3 = sin45/y
or, 1/√2/3 = 1/√2/y
or, y = 3
Now,
sinC/c = sinA/a
or, sin90/x sin45/3
or, 1/x = 1/√2/3
or, 1/x = 1/3√2
so, x = 3/√2