Question

practice solving problems involving complementary and supplementary angles. which angle pairs are supplementary? check all that apply. ∠1 and ∠2 ∠4 and ∠3 ∠4 and ∠5 ∠7 and ∠5 ∠3 and ∠6

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze each pair

• For \(\angle1\) and \(\angle2\):

They are adjacent and form a linear - pair. By the linear - pair postulate, \(\angle1+\angle2 = 180^{\circ}\).

• For \(\angle4\) and \(\angle3\):

They are adjacent and form a linear - pair. So, \(\angle4+\angle3=180^{\circ}\).

• For \(\angle4\) and \(\angle5\):

\(\angle4+\angle5 = 180^{\circ}\) (they form a linear - pair).

• For \(\angle7\) and \(\angle5\):

There is no information to suggest that \(\angle7+\angle5=180^{\circ}\).

• For \(\angle3\) and \(\angle6\):

\(\angle3+\angle6
eq180^{\circ}\) (they are vertical angles, \(\angle3=\angle6\)).

Answer:

\(\angle1\) and \(\angle2\), \(\angle4\) and \(\angle3\), \(\angle4\) and \(\angle5\)