adjacent
angles that share a side
congruent
angles with the same
measure.
supplementary
2 angles whose sum is 180°
vertical
opposite angles
made by two
intersecting lines
complementary
2 angles whose sum 90°
linear pair
2 angles that form a line.
7. name two linear pairs.
8. name two pairs of adjacent angles.
9. name one pair of complementary angles.
10. state one pair of vertical angles.
11. name one pair of supplementary angles.

Question

Accepted Answer

### Question 7: Name two linear pairs.
# Brief Explanations:
A linear pair consists of two adjacent angles that form a straight line (sum to $180^\circ$). From the diagram, $\angle LKM$ and $\angle MKN$ form a line? Wait, no, looking at the intersection at $K$. Let's identify:
1. $\angle LKP$ and $\angle PK O$? No, better: $\angle LKM$ and $\angle MK N$? Wait, the right angle is at $K$ between $L$ and $P N$? Wait, the diagram has $P - K - N$ as a straight line, $L - K - O$ as another? Wait, no, the vertical line is $L - K$ with a right angle to $P - N$. So linear pairs:
- $\angle LKP$ and $\angle LKN$? No, wait, linear pair is two angles forming a line. So $\angle LKM$ and $\angle MK N$ (but $\angle MK N$ is adjacent? Wait, maybe $\angle PK L$ and $\angle LKN$? No, let's re-express. A linear pair is two angles adjacent and forming a straight line. So:
1. $\angle LKP$ and $\angle PK O$ (but $P - K - O$ is a straight line? Wait, the diagram has $P$, $K$, $N$ on a horizontal line, and $L$, $K$, $O$ on a line? Wait, no, $P$ and $O$ are on one line, $N$ and... Wait, the intersection: $P - K - N$ (horizontal), $L - K - O$ (another line, with $L$ up, $O$ down). Also, $M$ is on a line from $K$ to $M$. So linear pairs:
- $\angle LKM$ and $\angle MK N$ (no, $\angle MK N$ is with $M$ and $N$). Wait, better:
1. $\angle PK L$ and $\angle LKN$: $P - K - N$ is straight, $L$ is up, so $\angle PK L$ (between $P - K - L$) and $\angle LKN$ (between $L - K - N$) form a line? No, $\angle PK L$ is a right angle? Wait, the right angle is at $K$ between $L$ and $P N$, so $\angle LKP = 90^\circ$, $\angle PKN = 90^\circ$? Wait, maybe I misread. Let's correct:
Linear pairs are two angles adjacent, sharing a side, and forming a straight line. So:
- $\angle LKM$ and $\angle MK N$ (no, $\angle MK N$ is adjacent? Wait, maybe $\angle PK L$ and $\angle LKN$ (but $\angle LKN$ is $90^\circ + \angle MK N$? No, let's take two angles that form a line. So:
1. $\angle PK O$ and $\angle OK N$ (but $P - K - N$ is straight, $O$ is below $K$, so $\angle PK O$ and $\angle OK N$ form a line? Wait, $P - K - N$ is horizontal, $O$ is on the line through $P$ and $O$, so $P - K - O$ is a straight line? No, $P$ and $O$ are on opposite sides of $K$, so $P - K - O$ is a straight line. So $\angle LKP$ and $\angle LKO$ (no, $L - K - O$ is a straight line? $L$ is up, $O$ is down, so $L - K - O$ is a straight line. So:
- $\angle LKP$ and $\angle PK O$: No, better examples:
1. $\angle LKM$ and $\angle MK N$ (wait, $\angle MK N$ is adjacent to $\angle LKM$ and forms a line? No, $\angle LKM$ and $\angle MK N$ sum to... Wait, the right angle: $\angle LKP = 90^\circ$, so $\angle LKM + \angle MK P$? No, maybe I'm overcomplicating. Let's use the definition: two angles adjacent, sharing a common side, and their non-common sides form a straight line.
So two linear pairs:
1. $\angle LKP$ and $\angle LKN$ (but $\angle LKN$ is $90^\circ$ +... No, wait, $P - K - N$ is straight, $L - K$ is vertical (right angle), so $\angle LKP = 90^\circ$, $\angle LKN = 90^\circ$? No, that can't be. Wait, maybe $\angle PK M$ and $\angle MK N$? No, let's look at the other line: $M$ is on a line from $K$ to $M$, so $\angle LKM$ and $\angle MK O$? No, perhaps the correct linear pairs are:
- $\angle LKP$ and $\angle PK O$ (since $P - K - O$ is a straight line, and they share side $KP$).
- $\angle LKN$ and $\angle NKO$ (since $L - K - O$ is a straight line? No, $L - K - O$ is a line, so $\angle LKN$ and $\angle NKO$ share $KN$ and form $L - K - O$? Wait, maybe I made a mistake. Let's simplify: linear pairs are adjacent angles forming a straight line. So two examples:
1. $\angle LKM$ and $\angle MK N$ (if $L - K - M - N$ is a line? No, $M$ is on a different line. Wait, the diagram has $P - K - N$ (horizontal), $L - K$ (vertical), $M$ on a line from $K$ to $M$ (between $L$ and $N$). So $\angle LKM$ and $\angle MK N$ are adjacent and form a line? No, $\angle LKM + \angle MK N = 90^\circ + \angle MK N$? Wait, the right angle is $\angle LKP = 90^\circ$, so $\angle LKM$ is part of that. Maybe the answer is:
- $\angle PK L$ and $\angle LKN$ (but $\angle LKN$ is $90^\circ$, $\angle PK L$ is $90^\circ$, sum $180^\circ$, so they form a linear pair).
- $\angle PK O$ and $\angle OK N$ (sum $180^\circ$, adjacent).

# Answer:
1. $\angle PK L$ and $\angle LKN$
2. $\angle PK O$ and $\angle OK N$

### Question 8: Name two pairs of adjacent angles.
# Brief Explanations:
Adjacent angles share a common side and vertex, but do not overlap. From the diagram:
- $\angle LKM$ and $\angle MK P$ (share side $KM$, vertex $K$).
- $\angle LKP$ and $\angle PK M$ (share side $KP$, vertex $K$).

# Answer:
1. $\angle LKM$ and $\angle MK P$
2. $\angle LKP$ and $\angle PK M$

### Question 9: Name one pair of complementary angles.
# Brief Explanations:
Complementary angles sum to $90^\circ$. From the diagram, $\angle LKM$ and $\angle MK P$ (if $\angle LKP = 90^\circ$, then $\angle LKM + \angle MK P = 90^\circ$).

# Answer:
$\angle LKM$ and $\angle MK P$

### Question 10: State one pair of vertical angles.
# Brief Explanations:
Vertical angles are opposite angles formed by intersecting lines, congruent. From the diagram, lines $P - O$ and $N -...$ Wait, lines $P - K - N$ and $L - K - O$ intersect at $K$, so vertical angles are:
- $\angle PK L$ and $\angle NKO$ (opposite angles formed by intersecting lines $P - N$ and $L - O$).

# Answer:
$\angle PK L$ and $\angle NKO$

### Question 11: Name one pair of supplementary angles.
# Brief Explanations:
Supplementary angles sum to $180^\circ$. From the diagram, $\angle LKP$ and $\angle LKN$ (if $\angle LKP = 90^\circ$ and $\angle LKN = 90^\circ$, sum $180^\circ$) or $\angle PK M$ and $\angle MK O$ (sum $180^\circ$ as linear pair, but linear pairs are supplementary). So one pair: $\angle LKP$ and $\angle LKN$.

# Answer:
$\angle LKP$ and $\angle LKN$

(Note: Answers may vary based on the exact diagram interpretation, but these follow the angle definitions.)

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QUESTION IMAGE

Question

Explanation:

Question 7: Name two linear pairs.

Answer:

Question 8: Name two pairs of adjacent angles.