Question

given \\( \angle abc \\) and \\( \angle def \\) are supplementary and \\( \angle abc \\) and \\( \angle ghj \\) are supplementary, what can you conclude about the angles?

choose the correct answer below.

\\( \bigcirc \\) a. \\( m \angle def + m \angle ghj = 180 \\)

\\( \bigcirc \\) b. \\( m \angle def + m \angle ghj = 90 \\)

\\( \bigcirc \\) c. \\( m \angle def = m \angle ghj \\)

\\( \bigcirc \\) d. \\( m \angle abc = m \angle def \\) and \\( m \angle abc = m \angle ghj \\)

Explanation:

Step1: Use the definition of supplementary angles

If \(\angle ABC\) and \(\angle DEF\) are supplementary, then \(m\angle ABC + m\angle DEF=180^{\circ}\). So, \(m\angle DEF = 180 - m\angle ABC\).

Step2: Use the definition of supplementary angles again

If \(\angle ABC\) and \(\angle GHJ\) are supplementary, then \(m\angle ABC + m\angle GHJ = 180^{\circ}\). So, \(m\angle GHJ=180 - m\angle ABC\).

Step3: Compare the two expressions

Since \(m\angle DEF = 180 - m\angle ABC\) and \(m\angle GHJ = 180 - m\angle ABC\), we can conclude that \(m\angle DEF=m\angle GHJ\).

Answer:

C. \(m\angle DEF = m\angle GHJ\)