Answer :
(i) The size of angle x is 58⁰.
(ii) The size of angle y is 70⁰.
Step-by-step explanation :
From the given figure we conclude that:
∠EFB = ∠FGD = x⁰ (corresponding angles are equal)
∠FGD = ∠CGH (vertically opposite angles are equal)
x⁰ = 58⁰
∠FGD = ∠AFG = 58⁰ (alternate angles are equal)
Now we have to calculate the value of 'y'.
As we know that the sum of interior angle of a triangle is equal to 180⁰.
In ΔAGF,
∠GAF + ∠AFG + ∠FGA = 180⁰
52⁰ + 58⁰ + y = 180⁰
110⁰ + y = 180⁰
y = 180⁰ - 110⁰
y = 70⁰
Therefore, the value of size of angle x and angle y is 58⁰ and 70⁰ respectively.