In a geometric figure two intersecting lines create four angles, where ∠1

Question

In a geometric figure two intersecting lines create four angles, where  ∠1
  and  ∠3
  are a vertical pair. If  m∠1=(3x−25)°
  and  m∠3=104°
 , what is the value of  x
 ?

GPT-4o mini · Answer

To solve for $ x $ in the given problem, we can use the property of vertical angles, which states that vertical angles are equal. Since $ \angle 1 $ and $ \angle 3 $ are vertical angles, we have: $$ m\angle 1 = m\angle 3 $$ Substituting in the values given in the problem: $$ 3x - 25 = 104 $$ Now, we will solve for $ x $. 1. Add $ 25 $ to both sides: $$ 3x - 25 + 25 = 104 + 25 $$ This simplifies to: $$ 3x = 129 $$ 2. Next, divide both sides by $ 3 $: $$ x = \frac{129}{3} $$ Calculating the right-hand side gives: $$ x = 43 $$ Thus, the value of $ x $ is $ \boxed{43} $.