Answer:
x=108
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
m∠RQS≅m∠QLK -----> by corresponding angles
m∠KLM+m∠QLK=180° -----> by supplementary angles (consecutive interior angles)
we have that
m∠RQS=x° ----> given problem
so
m∠QLX=x°
m∠KLM=(x-36)° ----> given problem
substitute

<u><em>Answer:</em></u>
b.Each electrician charges a different base fee:
<u><em>Explanation:</em></u>
<u>Each of the equations has two parts:</u>
1- base fee that is independent of any variable (this would be the number that has no variable next to it)
2- an hourly rate depending on the number of hours x (this would be the number that has an x next to it)
<u>For the first electrician:</u>
y = 25x + 30
base fee = $30
hourly rate = $25
<u>For the second electrician:</u>
y = 30x + 25
base fee = $25
hourly rate = $30
<u>For the third electrician:</u>
y = 25x + 20
base fee = $20
hourly rate = $25
<u>Now, let's check the choices:</u>
<span><u>a.Each electrician charges a different hourly rate:</u>
</span>This is incorrect as electricians 1 and 3 charge the same hourly rate ($25)
<span><u>b.Each electrician charges a different base fee:</u>
This is correct as all three base fees are different ($30, $20 and $25)
</span><span><u>c.All three electricians charge the same hourly rate:</u>
This is incorrect as electrician 2 has a different hourly rate
</span><span><u>d. All three electricians charge the same base fee:</u>
This is incorrect as the base fees for the three electricians are different ($30, $25 and $20)
Hope this helps :)</span>
An isosceles triangle is a special type of triangle that has two equal sides. Consequently, the two base angles are also equal. Since the interior angles of a triangle should sum up to 180°, the general equation should be
180° = 2*Base angle + Vertex angle
Let the base angle be x. Thus, the vertex angle is equal to
Vertex angle = 4x - 6
Substituting,
180 = 2x + 4x - 6
x = 31°
Vertex angle = 4(31°) - 6
Vertex angle = 118°