The figure shows two intersecting lines. What is the value of x?
Since vertical angles are congruent, we can make the following equation:
(4x + 7)° = (7x - 35)°
We can remove the degree signs and parenthesees from both sides of the equation.
4x + 7 = 7x - 35
Subtract 4x from both sides, add 35 to both sides.
7 + 35 = 7x - 4x
Combine like terms.
42 = 3x
Divide both sides of the equation by 3
? = x
Since a 180° angle forms a straight line, we can make the following equation:
(4x + 7)° + (10x - 23)° = 180°
Remove the degree signs from every term, then we can drop the two
sets of parenthesees because there is only addition between them
4x + 7 + 10x - 23 = 180
Simplify the left side by combining like terms.
14x - 16 = 180
Add 16 to both sides.
14x = 196
Divide both sides of the equation by 14
x = ?