Question

complementary, supplementary & vertical angles practice
please fill in the blank with correct word or words.

1. vertical angles are ______.
2. angles that share a vertex and a common side are ______ angles.
3. the measures of complementary angles add up to ______.
4. the measures of supplementary angles add up to ______.
5. two adjacent angles that make a straight line are called a ______.

please complete the chart with the correct angle measures.
6.
7.
8.
9.

	angle	complement	supplement	vertical
6.	43°
7.		51°
8.			162°
9.				13°

Explanation:

Step1: Define vertical angles property

Vertical angles are congruent (equal in measure).

Step2: Define adjacent angles

Angles sharing vertex + side are adjacent.

Step3: Complementary angles sum rule

Complementary angles sum to $90^\circ$.

Step4: Supplementary angles sum rule

Supplementary angles sum to $180^\circ$.

Step5: Define linear pair

Adjacent straight-line angles are linear pair.

Step6: Calculate complement for $43^\circ$

$\text{Complement} = 90^\circ - 43^\circ = 47^\circ$

Step7: Calculate supplement for $43^\circ$

$\text{Supplement} = 180^\circ - 43^\circ = 137^\circ$

Step8: Calculate angle for $51^\circ$ complement

$\text{Angle} = 90^\circ - 51^\circ = 39^\circ$

Step9: Calculate supplement for $39^\circ$

$\text{Supplement} = 180^\circ - 39^\circ = 141^\circ$

Step10: Calculate angle for $162^\circ$ supplement

$\text{Angle} = 180^\circ - 162^\circ = 18^\circ$

Step11: Calculate complement for $18^\circ$

$\text{Complement} = 90^\circ - 18^\circ = 72^\circ$

Step12: Calculate supplement for $13^\circ$ vertical angle

$\text{Supplement} = 180^\circ - 13^\circ = 167^\circ$

Step13: Calculate complement for $13^\circ$ vertical angle

$\text{Complement} = 90^\circ - 13^\circ = 77^\circ$

Step14: Angle = vertical angle measure

$\text{Angle} = 13^\circ$

Answer:

1. congruent (equal in measure)
2. adjacent
3. $90^\circ$
4. $180^\circ$
5. linear pair

Completed Chart:

Angle	Complement	Supplement	Vertical
$39^\circ$	$51^\circ$	$141^\circ$	$39^\circ$
$18^\circ$	$72^\circ$	$162^\circ$	$18^\circ$
$13^\circ$	$77^\circ$	$167^\circ$	$13^\circ$