Question

if ∠c + ∠d = 180, and ∠e and ∠d = 180, then ________. *
your answer

if ∠3 + ∠8 = 180, and ∠4 + ∠8 = 180, then ________. *
your answer

if x is parallel to y, and z is parallel to y, then ________. *
your answer

if ∠l ≅ ∠m, and ∠m is supplementary to ∠p, then ________. *
your answer

if ∠g is supplementary to ∠h, and ∠h ≅ ∠i, then ________

Explanation:

Step1: Use the property of supplementary angles

If two angles are supplementary to the same angle, they are equal.
Since \(\angle C+\angle D = 180^{\circ}\) and \(\angle E+\angle D=180^{\circ}\), then \(\angle C=\angle E\)

Step2: Use the property of supplementary angles

If two angles are supplementary to the same angle, they are equal.
Since \(\angle3+\angle8 = 180^{\circ}\) and \(\angle4+\angle8 = 180^{\circ}\), then \(\angle3=\angle4\)

Step3: Use the transitive property of parallel lines

If line \(X\parallel Y\) and line \(Z\parallel Y\), then \(X\parallel Z\) (transitive property of parallel lines: if \(a\parallel b\) and \(b\parallel c\), then \(a\parallel c\))

Step4: Use the definition of supplementary angles and congruent angles

If \(\angle L\cong\angle M\) and \(\angle M + \angle P=180^{\circ}\), then \(\angle L+\angle P = 180^{\circ}\) (substitution property)

Step5: Use the definition of supplementary angles and congruent angles

If \(\angle G+\angle H=180^{\circ}\) and \(\angle H\cong\angle I\), then \(\angle G+\angle I=180^{\circ}\) (substitution property)

Answer:

\(\angle C=\angle E\); \(\angle3=\angle4\); \(X\parallel Z\); \(\angle L+\angle P = 180^{\circ}\); \(\angle G+\angle I=180^{\circ}\)