Finding unkown angles
Since the angles given by the equation are alternate interior angles the are the same, that is
9x + 41 = 13x - 15
Using this equation, we can find x value
Step 1
Rearraging the equation so the terms with the unkown variable x are on the right side and the other ones on the left side:
9x + 41 = 13x - 15
↓ substracting 9x both sides
41 = -9x + 13x - 15
41 = 4x - 15
↓ adding 15 both sides
41 + 15= 4x
56 = 4x
Step 2
Solving the equation for x
56 = 4x
↓ dividing by 4 both sides
56/4 = x
14 = x
Answer A: x = 14
Now we want to find angle 4. Since it makes a straight line with the angle given by the expression 13x - 15, then their addition should be equal to 180°:
∡4 + 13x - 15 = 180
We want to find ∡4, and we do know the value for x, so, using the expression we can find it.
Replacing x by 14:
∡4 + 13x - 15 = 180
↓replacing x = 14
∡4 + 13 · 14 - 15 = 180
∡4 + 182 - 15 = 180
∡4 + 167 = 180
We follow the same previous steps to find ∡4
Step 1
Rearraging the equation so the terms with the unkown variable ∡4 are on the left side and the other ones on the right side:
∡4 + 167 = 180
↓ substracting 167 both sides
∡4 = - 167 + 180
∡4 = 13°
Step 2:We already found it using step 1 so step 2 is not neccesary to be followed
Answer B: ∡4 = 13°