Question

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

Explanation:

Step1: Recall supplementary - angle definition

Supplementary angles add up to 180 degrees. So, \(m\angle ABC + m\angle DEF=180^{\circ}\) and \(m\angle ABC + m\angle GHI = 180^{\circ}\).

Step2: Set up equations

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

Step3: Solve for \(y\) and \(z\)

From \(x + y=180\), we get \(y = 180 - x\). From \(x+z = 180\), we get \(z = 180 - x\). So, \(y = z\), which means \(m\angle DEF=m\angle GHI\).

Answer:

D. \(m\angle DEF = m\angle GHI\)