Geometry Practice Test 5

Property of centroid
AG = BC
2 GM = BC
Where m is the midpoint of BC.
∠1 = ∠3
And ∠2 = ∠4
∠1+∠2 = ∠3+∠4
i.e., ∠BGC = ∠3+∠4

As the sum of all the three angles is 180°,
BM = MC = MG
∠1+∠2 = 180° − (∠3+∠4)
∠1+∠2 = 180° − (2x)
2x = 180° − 2x
4x = 180
x = 45° ⇒ ∠BGC = 2x = 90°