Answer: x = -4, m∠XFH = 59°
Step-by-step explanation:
These angles given are vertical angles, meaning that they are congruent by definition.
Given:
-2x° + 113° = 12x° + 169°
Subtract 113 and 12x from both sides of the equation:
-14x° = 156°
Divide both sides of the equation by -14:
x = -4
Next, we can write an equation representing ∠XFH, substitute the value of x in, and simplify it to solve. Note that a straight angle is equal to 180 degrees.
Given:
180° = -2x° + 113° + m∠XFH
Substitute known values:
180° = -2(-4)° + 113° + m∠XFH
Simplify:
180° = 121° + m∠XFH
Subtract 121 from both sides of the equation:
59° = m∠XFH