Question

1. b = x + 30, h = 5x - 14

type of angle pair _ relation _ x = _

1. a = 10x - 30, e = 8x + 20

type of angle pair _ relation _ x = _

Explanation:

Step1: Analyze the angle pair relationship for problem 29

Assuming \(b\) and \(h\) are alternate interior angles (since \(b=x + 30\) and \(h=5x-14\) and the hand - written "AH" might stand for alternate interior angles). Alternate interior angles are congruent. So we set up the equation \(x + 30=5x-14\).

Step2: Solve the equation for problem 29

Subtract \(x\) from both sides: \(30 = 4x-14\). Then add 14 to both sides: \(44=4x\). Divide both sides by 4: \(x = 11\).

Step3: Analyze the angle pair relationship for problem 30

Assuming \(a\) and \(e\) are corresponding angles (since the hand - written "Corr" might stand for corresponding angles). Corresponding angles are congruent. So we set up the equation \(10x-30=8x + 20\).

Step4: Solve the equation for problem 30

Subtract \(8x\) from both sides: \(2x-30=20\). Then add 30 to both sides: \(2x=50\). Divide both sides by 2: \(x = 25\).

Answer:

For problem 29: \(x = 11\)
For problem 30: \(x = 25\)