Question

name:
use the figure at the right to answer problems 1 - 8.
classify each pair of angles as one of the following:
(a) alternate interior angles (b) corresponding angles
(c) alternate exterior angles (d) vertical angles
(e) supplementary angles (f) none

1. _ $angle 9$ & $angle 16$ 5. _ $angle 9$ & $angle 11$
2. _ $angle 15$ & $angle 11$ 6. _ $angle 9$ & $angle 15$
3. _ $angle 10$ & $angle 15$ 7. _ $angle 13$ & $angle 14$
4. _ $angle 12$ & $angle 15$ 8. _ $angle 14$ & $angle 11$
5. $mangle 2 = 97^circ$ $mangle 6 = 83^circ$

$mangle 3 = _____$ $mangle 5 = _____$
$mangle 10 = _____$ $mangle 7 = _____$
$mangle 9 = _____$ $mangle 16 = _____$
find the value of x given that $s parallel t$

1. $mangle 4 = 77^circ$, $mangle 8 = 4x + 57$
2. $mangle 3 = 5x + 13$, $mangle 5 = 53^circ$
3. $mangle 1 = 6x - 5$, $mangle 7 = 115^circ$

Explanation:

Step1: Identify Angle Relationship

Since \( s \parallel t \), \( \angle 4 \) and \( \angle 8 \) are corresponding angles (or alternate exterior, etc.), so \( m\angle 4 = m\angle 8 \). Wait, no—wait, \( \angle 4 \) and \( \angle 8 \): Wait, looking at the diagram (for problem 10), \( \angle 4 \) and \( \angle 8 \) are actually... Wait, no, maybe \( \angle 4 \) and \( \angle 8 \) are equal? Wait, no, wait: \( s \parallel t \), and the transversal. Wait, \( \angle 4 \) and \( \angle 8 \): Wait, maybe \( \angle 4 \) and \( \angle 8 \) are corresponding? Wait, no, let's recheck. Wait, \( m\angle 4 = 77^\circ \), and \( m\angle 8 = 4x + 57 \). Wait, maybe they are equal? Wait, no, maybe supplementary? Wait, no, let's see the diagram. Wait, in the diagram for problem 10, the lines \( s \) and \( t \) are parallel, cut by a transversal. So \( \angle 4 \) and \( \angle 8 \): Wait, \( \angle 4 \) is on line \( t \)'s upper side, \( \angle 8 \) is on line \( s \)'s lower? Wait, no, maybe \( \angle 4 \) and \( \angle 8 \) are equal (corresponding angles). Wait, if \( s \parallel t \), then corresponding angles are equal. So \( m\angle 4 = m\angle 8 \). So \( 77 = 4x + 57 \).

Step2: Solve for \( x \)

Set up the equation: \( 4x + 57 = 77 \).
Subtract 57 from both sides: \( 4x = 77 - 57 = 20 \).
Divide by 4: \( x = \frac{20}{4} = 5 \).

Answer:

\( x = 5 \)