Answer:
∠B = 60
Explanation:
Finding the value of x
In order to find the measure of ∠B we must first find the value of x
We 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 angles
According to the exterior angle rule ∠BCG would equal ∠B + A
We have ∠BCG = 10x - 45 , ∠A = 3x and ∠B = 4x
Plugging the values of the angles into ∠BCG = ∠B + ∠A
We acquire 10x - 45 = 3x + 4x , we now solve for x
==> combine like terms
10x - 45 = 7x
==> add 45 to both sides
10x = 7x + 45
==> subtract 7x from both sides
3x = 45
==> divide both sides by x
x = 15
Finding the measure of ∠B
We can do this by plugging in the value of x into the expression given by ∠B
We have ∠B = 4x
==> plug in x = 15
∠B = 4(15)
==> multiply 4 and 15
∠B = 60