Answer: x = 20, ∠7 = 82°
Explanation:
It is given that ∠8 and ∠4 are corresponding angles. This means that they are congruent. We can set them equal to each other to solve for x.
Given:
7x - 42 = 3x + 38
Add 42 to both sides of the equation:
7x = 3x + 80
Subtract 3x from both sides of the equation:
4x = 80
Divide both sides of the equation by 4:
x = 20
Next, we can use this value of x to help us solve for ∠7. We know that a straight line is equal to 180 degrees, so ∠7 + ∠8 = 180°.
Given:
∠7 + ∠8 = 180°
Substiute angle 8:
∠7 + 7x - 42° = 180°
Substiute x:
∠7 + 7(20)° - 42° = 180°
Compute:
∠7 + 98° = 180°
Subtract 98° from both sides of the equation:
∠7 = 82°