Question

which equation is correct? image of two intersecting lines forming angles 1 and 2 options: ▲ m∠1 + m∠2 = 180, ● m∠1 = m∠2, ◆ m∠1 + m∠2, ■ m∠1 + m∠2 = 90

Explanation:

Step1: Identify Angle Relationship

In the diagram, ∠1 and ∠2 are vertical angles? No, wait, they are adjacent and form a linear pair? Wait, no, looking at the intersection of two lines, ∠1 and ∠2—wait, actually, when two lines intersect, vertical angles are equal. Wait, the diagram shows two intersecting lines, so ∠1 and ∠2 are vertical angles? Wait, no, maybe I missee. Wait, the options: one is \( m\angle1 = m\angle2 \) (vertical angles are equal), another is \( m\angle1 + m\angle2 = 180^\circ \) (supplementary), \( m\angle1 + m\angle2 = 90^\circ \) (complementary), or \( m\angle1 + m\angle2 \) (incomplete). Wait, vertical angles are equal, so \( m\angle1 = m\angle2 \) is correct? Wait, no, wait the diagram: let me check again. The two lines intersect, so ∠1 and ∠2—if they are vertical angles, then they are equal. So the yellow option is \( m\angle1 = m\angle2 \), red is supplementary, green is complementary, blue is incomplete. So vertical angles are equal, so \( m\angle1 = m\angle2 \) is correct. Wait, but wait, maybe I made a mistake. Wait, when two lines intersect, vertical angles are congruent (equal measure). So the correct equation is \( m\angle1 = m\angle2 \).

Step2: Evaluate Options

• Red: \( m\angle1 + m\angle2 = 180^\circ \): This is for supplementary angles (linear pair), but ∠1 and ∠2 here are vertical angles, not a linear pair (unless they are adjacent and form a straight line, but in the diagram, they are vertical? Wait, maybe the diagram is two intersecting lines, so ∠1 and ∠2 are vertical angles, so equal. So red is wrong.
• Yellow: \( m\angle1 = m\angle2 \): Vertical angles are equal, so this is correct.
• Green: \( m\angle1 + m\angle2 = 90^\circ \): Complementary, not applicable here.
• Blue: \( m\angle1 + m\angle2 \): Incomplete, not an equation.

So the correct option is the yellow one: \( m\angle1 = m\angle2 \).

Answer:

The yellow option: \( m\angle1 = m\angle2 \)