Answer: x = 7°, m∠IED = 42°
Step-by-step explanation:
These angles given are corresponding angles, meaning that they are congruent by definition.
Given:
-3x° + 159° = -5x° + 173°
Subtract 159 from both sides of the equation:
-3x° = -5x° + 14°
Add 5x to both sides of the equation:
2x° = 14°
Divide both sides of the equation by 2:
x = 7°
Next, we can write an equation representing ∠IED, substitute the value of x in, and simplify it to solve. Note that a straight angle is equal to 180 degrees.
Given:
180° = -3x° + 159° + m∠IED
Substitute known values:
180° = -3(7)° + 159° + m∠IED
Simplify:
180° = 138° + m∠IED
Subtract 138 from both sides of the equation:
42° = m∠IED