Question

H is the interior of <JAK. <JAH=3x-8 degrees and <KAH= x+2 degrees. What is the measure of all angles?

Answer 1

In this problem, we could use the Angle Addition Postulate property. This property states that all interior angles within should sum of to the total angle. It is specifically stated that point H is interior of angle ∠JAK. Looking at the diagram attached in the picture, line segment AH is drawn in the middle. Therefore, the Angle Addition Postulate tells us that the sum of interior angles JAH and angle HAK, is equal to the total angle JAK. 

∠JAK = ∠JAH + ∠HAK
∠JAK = (3x - 8) + (x+2)

But there is a missing information. Without knowing the total angle JAK, we can't solve for x. Consequently, we can't solve for the interior angles. So, let's just assume that ∠JAK = 45°. This is just for sample purposes. 

45° = (3x - 8) + (x+2)
45 = 4x - 6
4x = 45+6
4x = 51
x = 12.75°

Therefore, the interior angles are equal to
∠JAH = 3(12.75) - 8 = 30.25°
∠HAK = 12.75 + 2 = 14.75°