Answer:
[tex]113\° = \angle A[/tex]
Step-by-step explanation:
Given:
- ∠A = ∠B (Vertically opposite angles)
- ∠A = 7x - 20
- ∠B = 6x - 1
If ∠A is equivalent to ∠B, then...
[tex]\implies 7x - 20 = 6x - 1[/tex]
Add 1 both sides:
[tex]\implies 7x - 20 + 1= 6x - 1 + 1[/tex]
Simplify both sides:
[tex]\implies 7x - 19= 6x[/tex]
Subtract 7x both sides:
[tex]\implies 7x- 7x - 19= 6x - 7x[/tex]
Simplify both sides:
[tex]\implies -19= -x[/tex]
Divide both sides by -1:
[tex]\implies \dfrac{-19}{-1} = \dfrac{-x}{-1}[/tex]
Simplify both sides:
[tex]\implies 19= x[/tex]
Substitute the value of x into "7x - 20" to determine ∠A:
[tex]\implies 7x - 20 = \angle A[/tex]
[tex]\implies 7(19) - 20 = \angle A[/tex]
Simplify the expression:
[tex]\implies 133 - 20 = \angle A[/tex]
[tex]\implies 113\° = \angle A[/tex]
