Question

lesson 8.2p ~ vertical and adjacent angles
name _______________________ period __ date ____

1. determine the measure of each unknown angle using the diagram below.

a. $m\angle2 = \underline{106^\circ}$
b. $m\angle3 = \underline{74^\circ}$
c. $m\angle4 = \underline{106^\circ}$
(accompanying diagram with intersecting lines labeled 2, 3, 4 and a $106^\circ$ angle)

1. sketch and label a diagram to represent each situation.

$\angle1$ and $\angle3$ are acute vertical angles.

1. $\angle5$ and $\angle6$ are adjacent angles.

$\angle5$ is an obtuse angle.

1. identify each angle pair as adjacent angles, vertical angles or a linear pair. solve for $x$.

(accompanying diagram with intersecting lines, one angle labeled $48^\circ$, its vertical angle labeled $(5x + 2)^\circ$)

1. identify each angle pair as adjacent angles, vertical angles or a linear pair. solve for $x$.

(accompanying diagram with angles labeled $36^\circ$ and $3x^\circ$ formed by intersecting lines)

Explanation:

Step1: Find $m\angle2$ (vertical angle)

Vertical angles are equal, so $m\angle2 = 106^\circ$

Step2: Find $m\angle3$ (linear pair)

Linear pair sums to $180^\circ$, so $m\angle3 = 180^\circ - 106^\circ = 74^\circ$

Step3: Find $m\angle4$ (vertical angle)

Vertical angles are equal, so $m\angle4 = m\angle3 = 74^\circ$

Step4: Solve for $x$ (Q4, vertical angles)

Vertical angles are equal: $5x + 2 = 48$
$5x = 48 - 2 = 46$
$x = \frac{46}{5} = 9.2$

Step5: Solve for $x$ (Q5, linear pair)

Linear pair sums to $180^\circ$: $3x + 36 = 180$
$3x = 180 - 36 = 144$
$x = \frac{144}{3} = 48$

Answer:

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

1. (Diagram: Two intersecting lines forming four angles; label non-adjacent acute angles as $\angle1$ and $\angle3$)
2. (Diagram: Two lines meeting at a vertex, forming adjacent angles; label the larger (obtuse) angle as $\angle5$ and the smaller as $\angle6$)
3. $x = 9.2$
4. $x = 48$