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<span>It is important to know that the sum of the three angles inside a triangle add up to 180 degrees. So then we get the following by adding up all three provided angle measures:
3x + (2x + 20) + (4x - 20) = 180
Some algebraic manipulation follows:
3x + 2x + 20 + 4x - 20 = 180
9x = 180
x = 180/9 = 20
The value of x is 20 degrees.</span>
Answer:
c = 12.5
Step-by-step explanation:
This is a right triangle so we can use the Pythagorean theorem (a^2 + b^2 = c^2)
lets say 10 = a and 7.5 = b (this is because they are the legs of the triangle and variables a and b represent the legs of the triangle)
plug into the Pythagorean theorem.
10^2 + 7.5^2 = c^2
simplify (here you just square 10 and 7.5)
100 + 56.25 = c^2
simplify
156.25 = c^2
simplify
(here you get the square root of 156.25 and c^2, the positive square root of 156.25 is 12.5 and the square root of c^2 is c)
12.5 = c
Parallel lines have the same slope, so since you want a line that is parallel to a line with slope -8, your line will also have slope -8.
The slope-intercept form of the equation of a line is
y = mx + b
where m is the slope, and b is the y-intercept.
You already know you have a slope of -8, so m = -8, and you have
y = -8x + b
Now you need to find the value of b.
Use the point you know and substitute it in for x and y, and solve for b.
y = -8x + b
Use x = -8, and y = 2.
2 = -8(-8) + b
2 = 64 + b
-62 = b
b = -62
Now replace b with -62.
y = -8x + b
y = -8x - 62
