Question

1. if m∠4=(2x + 10)° and m∠6=(3x - 20)°, find the value of x.
2. if m∠2=(3x + 15)° and m∠6=(5x - 5)°, find the value of x.
3. if m∠3=(2x + 40)° and m∠6=(3x + 20)°, find the value of x.

Explanation:

Step1: Assume angles are equal (if applicable)

For parallel - line related angle problems, if the angles are corresponding, alternate - interior, etc., they are equal. Here we assume the pairs of angles are equal.

Step2: Set up the equation

For question 14:
Set \(2x + 10=3x - 20\).

Step3: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(10=x - 20\).
Then add 20 to both sides: \(x=30\).

For question 15:
Set \(3x + 15 = 5x-5\).
Subtract \(3x\) from both sides: \(15 = 2x-5\).
Add 5 to both sides: \(20 = 2x\).
Divide both sides by 2: \(x = 10\).

For question 16:
Set \(2x+40=3x + 20\).
Subtract \(2x\) from both sides: \(40=x + 20\).
Subtract 20 from both sides: \(x = 20\).

Answer:

1. \(x = 30\)
2. \(x = 10\)
3. \(x = 20\)