Question

lesson 8.2p ~ vertical and adjacent angname_______________________ period_____1. determine the measure of each unknown angle using the diagram below.a. $mangle2 =$b. $mangle3 =$c. $mangle4 =$sketch and label a diagram to represent each situation.2. $angle1$ and $angle3$ are acute vertical angles.3. $angle5$ and $angle6$ are adjacent angles.$angle5$ is an obtuse angle.identify each angle pair as adjacent angles, vertical angles or a linear pair. solve for $x$.4. $(5x + 2)^circ$, $48^circ$5. $3x^circ$, $36^circ$6. $56^circ$, $(8 - 2x)^circ$7. $(4x - 7)^circ$, $(x + 16)^circ$, $68^circ$

Explanation:

Step1: Solve Q1a (Vertical angles congruent)

$m\angle2 = 106^\circ$

Step2: Solve Q1b (Linear pair sum to 180°)

$m\angle3 = 180^\circ - 106^\circ = 74^\circ$

Step3: Solve Q1c (Vertical angles congruent)

$m\angle4 = m\angle3 = 74^\circ$

Step4: Solve Q4 (Vertical angles congruent)

$5x + 2 = 48$
$5x = 48 - 2 = 46$
$x = \frac{46}{5} = 9.2$

Step5: Solve Q5 (Linear pair sum to 180°)

$3x + 36 = 180$
$3x = 180 - 36 = 144$
$x = \frac{144}{3} = 48$

Step6: Solve Q6 (Vertical angles congruent)

$8 - 2x = 56$
$-2x = 56 - 8 = 48$
$x = \frac{48}{-2} = -24$

Step7: Solve Q7 (Angle addition postulate)

$(4x - 7) - (x + 16) = 68$
$4x -7 -x -16 = 68$
$3x -23 = 68$
$3x = 68 + 23 = 91$
$x = \frac{91}{3} \approx 30.33$

Step8: Sketch Q2 (Acute vertical angles)

Draw two intersecting lines, label opposite acute angles as $\angle1$ and $\angle3$ (both <90°).

Step9: Sketch Q3 (Obtuse adjacent angles)

Draw a shared ray between two rays forming an obtuse $\angle5$, label the adjacent angle as $\angle6$ (sharing the side and vertex with $\angle5$, $\angle5$ >90°).

Answer:

1.
a. $m\angle2 = 106^\circ$
b. $m\angle3 = 74^\circ$
c. $m\angle4 = 74^\circ$

1. (Diagram: Two intersecting lines with opposite acute angles labeled $\angle1$ and $\angle3$)
2. (Diagram: A common vertex with three rays, where the two outer rays form obtuse $\angle5$, and the middle ray forms adjacent $\angle6$ with one outer ray)
3. $x = 9.2$
4. $x = 48$
5. $x = -24$
6. $x = \frac{91}{3}$