Question

for *3, use the figure at the right.
a) name two acute vertical angles.
b) name two obtuse vertical angles.
c) name a linear pair.
d) name two acute adjacent angles.
e) name an angle complementary to ∠fkg.
f) name an angle supplementary to ∠fkg.

Explanation:

Step1: Recall angle - pair definitions

Vertical angles are opposite each other when two lines intersect. Acute angles are less than 90°, obtuse angles are between 90° and 180°, linear - pairs are adjacent angles that form a straight line, adjacent angles share a common side and a common vertex, complementary angles add up to 90°, and supplementary angles add up to 180°.

Step2: Identify acute vertical angles

Looking at the figure, assume $\angle EKH$ and $\angle GKF$ are acute vertical angles as they are opposite each other and appear to be less than 90°.

Step3: Identify obtuse vertical angles

$\angle EKG$ and $\angle HKF$ are obtuse vertical angles since they are opposite each other and are greater than 90° and less than 180°.

Step4: Identify a linear - pair

$\angle EKH$ and $\angle EKG$ form a linear - pair as they are adjacent and their non - common sides form a straight line.

Step5: Identify acute adjacent angles

$\angle FKG$ and $\angle GKJ$ are acute adjacent angles as they share a common side $KG$ and a common vertex $K$ and are less than 90°.

Step6: Identify a complementary angle to $\angle FKG$

If $\angle FKG$ is acute, assume $\angle GKJ$ is complementary to $\angle FKG$ such that $\angle FKG+\angle GKJ = 90^{\circ}$.

Step7: Identify a supplementary angle to $\angle FKG$

$\angle EKG$ is supplementary to $\angle FKG$ since $\angle FKG+\angle EKG=180^{\circ}$ (they form a linear - pair).

Answer:

a) $\angle EKH$ and $\angle GKF$
b) $\angle EKG$ and $\angle HKF$
c) $\angle EKH$ and $\angle EKG$
d) $\angle FKG$ and $\angle GKJ$
e) $\angle GKJ$
f) $\angle EKG$