Question

3.

• ∠1 and ∠4 are
• ∠4 and ∠5 are

and

• which angle is complementary to ∠2?
• which angles are adjacent to ∠3?

Explanation:

Step1: Identify vertical angles

Vertical angles are opposite angles formed by two intersecting lines. $\angle1$ and $\angle4$ are vertical angles.

Step2: Identify linear - pair and vertical angles

$\angle4$ and $\angle5$ form a linear - pair (sum to $180^{\circ}$). $\angle4$ and $\angle2$ are vertical angles (so $\angle2=\angle4$), and $\angle5$ and $\angle6$ are vertical angles.

Step3: Find complementary angle

Complementary angles sum to $90^{\circ}$. Since $\angle3 = 90^{\circ}$ and $\angle2+\angle1=\angle3$ (because of the right - angle), $\angle1$ is complementary to $\angle2$.

Step4: Identify adjacent angles

Adjacent angles share a common side and a common vertex. $\angle2$ and $\angle4$ are adjacent to $\angle3$.

Answer:

• $\angle1$ and $\angle4$ are vertical angles.
• $\angle4$ and $\angle5$ are a linear - pair and $\angle4$ and $\angle2$ (or $\angle5$ and $\angle6$) are vertical angles.
• The angle complementary to $\angle2$ is $\angle1$.
• The angles adjacent to $\angle3$ are $\angle2$ and $\angle4$.