Question

all linear angle pairs are also supplementary angle pairs. although all supplementary angle pairs do not need to be linear angle pairs.
linear angle pair fact
exercise #3: in the diagram shown below, lines l, m, and n intersect to form ∠1, ∠2, ∠3, and ∠4 (as well as others). if m∠2 = m∠3 = 30°, then do the following:
(a) determine m∠1 and m∠4.
(b) name a pair of supplementary angles that are also a linear pair.
(c) name a pair of supplementary angles that are not also a linear pair.
our final type of angle pair is one we have explored some already. it is also linked to when two lines cross each other. this type of pair is known as a vertical pair.
vertical angle pairs
vertical angles are any two angles that share a common vertex and whose rays point in opposite directions. vertical angles are created when two lines cross each other.
exercise #4: line m and n intersect below to form the four marked angles. answer the following.
(a) list the two pairs of vertical angles.
(b) explain why m∠1 + m∠2 = m∠2 + m∠3.
(c) how does the equation in (b) allow you to conclude that m∠1 = m∠3?
vertical angle pair fact
vertical angles pairs will have the same degree measure. in other words, vertical angles are congruent.
n - gen math geometry - unit 1 - beginning concepts - lesson 6
emathinstruction, red hook, ny 12571, © 2023

Explanation:

Exercise #3

(a)

Step1: Use linear - angle pair property

Since $\angle1$ and $\angle2$ form a linear - angle pair, $m\angle1 + m\angle2=180^{\circ}$. Given $m\angle2 = 30^{\circ}$, then $m\angle1=180^{\circ}-m\angle2$.
$m\angle1 = 180 - 30=150^{\circ}$

Step2: Use linear - angle pair property for $\angle3$ and $\angle4$

Since $\angle3$ and $\angle4$ form a linear - angle pair, $m\angle3 + m\angle4=180^{\circ}$. Given $m\angle3 = 30^{\circ}$, then $m\angle4=180^{\circ}-m\angle3$.
$m\angle4 = 180 - 30=150^{\circ}$

$\angle1$ and $\angle2$ form a linear - angle pair, so $m\angle1 + m\angle2=180^{\circ}$. $\angle2$ and $\angle3$ form a linear - angle pair, so $m\angle2 + m\angle3=180^{\circ}$. Since both sums equal $180^{\circ}$, $m\angle1 + m\angle2=m\angle2 + m\angle3$.

If $m\angle1 + m\angle2=m\angle2 + m\angle3$, we can subtract $m\angle2$ from both sides of the equation. Using the subtraction property of equality, $(m\angle1 + m\angle2)-m\angle2=(m\angle2 + m\angle3)-m\angle2$, which simplifies to $m\angle1=m\angle3$.

Answer:

$m\angle1 = 150^{\circ}$, $m\angle4 = 150^{\circ}$

(b)