Look at the picture.
Corresponding Angles are equal.
Alternate Angles are equal.
Consecutive Angles add up to 180°.
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3a and 45 are Consecutive Angles. Therefore
3a + 45 = 180 |subtract 45 from both sides
3a = 135 |divide both sides by 3
<h3>a = 45.</h3>
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(2c - 1) and 45 are Corresponding Angles. Therefore
2c - 1 = 45 |add 1 to both sides
2c = 46 |divide both sides by 2
<h3>c = 23.</h3>
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3a and (12b + 3) are Alternate Angles. Therefore
3(45) = 12b + 3
135 = 12b + 3 |subtract 3 from both sides
132 = 12b |divide both sides by 12
<h3>b = 11.</h3>
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Step-by-step explanation:
<h3>
Answer: perpendicular</h3>
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Work Shown:
Use the slope formula to find the slope of line AB
m = (y2-y1)/(x2-x1)
m = (f-0)/(e-0)
m = f/e
Let p = f/e so we can compare the slope later
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Use the slope formula to find the slope of line CD
m = (y2-y1)/(x2-x1)
m = (0-e)/(f-0)
m = -e/f
Let q = -e/f so we can compare the slope later
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We have
- p = f/e which is the slope of AB
- q = -e/f which is the slope of CD
Multiply the values of p and q
p*q = (f/e)*(-e/f) = (f(-e))/(ef) = (-ef)/(ef) = -1
since p*q = -1, this means the lines AB and CD are perpendicular. They form a 90 degree angle.
1.6
0.9
0.2
-0.8
-2.4
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