Question

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

Explanation:

Step1: Recall the definition of supplementary angles

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

From \(m\angle ABC + m\angle DEF=180^{\circ}\), we can get \(m\angle ABC=180 - m\angle DEF\). From \(m\angle ABC + m\angle GHI = 180^{\circ}\), we can get \(m\angle ABC=180 - m\angle GHI\).

Step3: Equate the two - expressions for \(m\angle ABC\)

Since \(180 - m\angle DEF=180 - m\angle GHI\), subtracting 180 from both sides gives \(-m\angle DEF=-m\angle GHI\), and then \(m\angle DEF = m\angle GHI\).

Answer:

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