Answer:
<d = 25 degrees and <e = 130 degrees
Step-by-step explanation:
We have a vertical angle, so the opposite sides of this angle are the same. This means that the angle opposite to 25 degrees also measures 25 degrees. We have one angle of the triangle. Since the triangle is isosceles, the angle d is the same as 25 degrees.
<d = 25 degrees
The interior angles of a triangle add up to 180 degrees, and we now have 2 angles, so:
<e = 180 - 25 - d
<e = 155-25
<e = 130 degrees
So,
Mark wants $100 for 10 hrs., or $10/hr.
Rick wants $80 for 9 hrs., or

$8.89/hr.
Steve wants $75 for 8 hrs., or $

/hr. or $9.38/hr.
Finally, Andy wants $60 for 5 hrs., or $12/hr.
We can see that <u>Rick</u> offers the best deal, at $8.89/hr.
<h3>
Answer: 40</h3>
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Explanation:
The inscribed angle 20 degrees doubles to 2*20 = 40 which is the measure of the central angle, and the arc in which the inscribed angle subtends (or cuts off). This is due to the aptly named inscribed angle theorem.
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A slightly longer alternative path would be to do this:
The triangle with interior angles 20 and c is isosceles. Note how the missing angle up top is one of the congruent base angles, so the missing angle is 20 degrees. That means angle c is...
20+20+c = 180
40+c = 180
c = 180-40
c = 140
Then angle b is supplementary to this
b+c = 180
b+140 = 180
b = 180-140
b = 40
This path leads to the same answer. It's slightly longer, but it's a path you can take if you aren't familiar with the inscribed angle theorem.
In fact, this line of thinking is effectively how the inscribed angle theorem is proved as shown in the diagram below.
0.5x + 1/5y -3.5x - 4/5 y
0.5x - 3.5x + 1/5 y - 4/5 y. Regroup f/ variable
-3.0x - 3/5 y
Answer:d
Step-by-step explanation: multiply -2 times -4