Question

which equation is correct? image of intersecting lines with angles 1 and 2 options: ▲ ( mangle1 + mangle2 = 180 ) ◆ ( mangle1 + mangle2 = 90 ) ● ( mangle1 + mangle2 ) ■ ( mangle1 = mangle2 )

Explanation:

Step1: Analyze the angle relationship

In the diagram, ∠1 and ∠2 are vertical angles. By the Vertical Angles Theorem, vertical angles are equal in measure. So \( m\angle1 = m\angle2 \).

Step2: Evaluate the options

• The red option (\( m\angle1 + m\angle2 = 180 \)) is for supplementary angles (linear pair), not vertical angles.
• The blue option (\( m\angle1 + m\angle2 = 90 \)) is for complementary angles, not applicable here.
• The yellow option (\( m\angle1 + m\angle2 \)) is not an equation.
• The green option (\( m\angle1 = m\angle2 \)) matches the vertical angles relationship.

Answer:

■ \( m\angle1 = m\angle2 \)