Answer:
∠1 = 47
∠2 = 63
∠3 = 70
∠4 = 70
Step-by-step explanation:
∠2 and 63 are alternate interior angles. Alternate interior angles are equal.
∠2 = 63
∠3 and 110 are linear pair angles. Sum of linear pair angles is 180.
∠3 + 110 = 180
∠3 = 180 - 110
∠3 = 70
GDEF is a parallelogram, so ∠DGF = ∠DEF
That is,
∠3 = ∠4
∠4 = 70
∠1, ∠2 and ∠3 are interior angles in a triangle.
Sum of interior angles in a triangle is 180,
∠1 + ∠2 + ∠3 = 180
∠1 + 63 + 70 = 180
∠1 + 133 = 180
∠1 = 180 - 133
∠1 = 47
