Question

question 14
03:07
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1. if

m∠1 = m∠6,
then
m∠1 = m∠8
∠1 ≅ ∠8
∠1 ≅ ∠6
m∠1 + m∠6 = 180°

Explanation:

Step1: Use the property of vertical angles

Vertical angles are congruent. So, \(\angle6\cong\angle8\) (because they are vertical angles).

Step2: Use the definition of congruent angles

If \(\angle6\cong\angle8\), then \(m\angle6 = m\angle8\) (by the definition of congruent angles: congruent angles have equal measures).

Step3: Substitute \(m\angle1\) for \(m\angle6\)

Given \(m\angle1 = m\angle6\), substitute \(m\angle6\) with \(m\angle1\) in \(m\angle6 = m\angle8\). We get \(m\angle1 = m\angle8\).

Answer:

\(m\angle1 = m\angle8\)