Answer:∠B = 60Step-by-step explanation:Finding the value of xIn order to find the measure of ∠B we must first find the value of xWe can do this by using the exterior angle rule.Exterior angle rule : An exterior angle of a triangle is equal to the sum of the opposite interior angles ( angles inside of the triangle excluding the one next to the exterior angle ) Here, we have ∠BCG as the exterior angle and ∠B and ∠A as the opposite interior anglesAccording to the exterior angle rule ∠BCG would equal ∠B + AWe have ∠BCG = 10x - 45 , ∠A = 3x and ∠B = 4xPlugging the values of the angles into ∠BCG = ∠B + ∠A We acquire 10x - 45 = 3x + 4x , we now solve for x ==> combine like terms10x - 45 = 7x==> add 45 to both sides10x = 7x + 45==> subtract 7x from both sides3x = 45==> divide both sides by xx = 15Finding the measure of ∠BWe can do this by plugging in the value of x into the expression given by ∠BWe have ∠B = 4x==> plug in x = 15∠B = 4(15)==> multiply 4 and 15∠B = 60