Question

given ∠abc and ∠def are supplementary and ∠abc and ∠ghj are supplementary, what can you conclude about the angles? choose the correct answer below. a. m∠def = m∠ghj b. m∠def + m∠ghj = 90 c. m∠abc = m∠def and m∠abc = m∠ghj d. m∠def + m∠ghj = 180

Explanation:

Step1: Recall supplementary - angle definition

Supplementary angles add up to 180 degrees. So, \(m\angle ABC + m\angle DEF=180\) and \(m\angle ABC + m\angle GHJ = 180\).

Step2: Set up equations

Let \(x = m\angle ABC\), \(y = m\angle DEF\), \(z = m\angle GHJ\). We have \(x + y=180\) and \(x + z = 180\). Then \(x + y=x + z\).

Step3: Solve for the relationship between \(y\) and \(z\)

Subtract \(x\) from both sides of the equation \(x + y=x + z\). We get \(y = z\), which means \(m\angle DEF=m\angle GHJ\).

Answer:

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