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Question 14, Part (i)
Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,
A+B+C+D = 360
A+90+C+90 = 360
A+C+180 = 360
A+C = 360-180
A+C = 180
Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.
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Question 14, Part (ii)
Let
x = measure of angle 1
y = measure of angle 2
z = measure of angle 3
Back in part (i) above, we showed that y + z = 180
Note that angles 1 and 2 are adjacent to form a straight line, so we can say
x+y = 180
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We have the two equations x+y = 180 and y+z = 180 to form this system of equations
Which is really the same as this system
The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.
Answer:
2 7/20
Step-by-step explanation:
So Lets put these into a fraction form
Petra: 5 3/5
Pauline: 3 4/16 -> Can be Simplified = 3 1/4
Take the number of pies Petra Ate and subtract it by the number of pies Pauline ate
Change the numbers to a common factor. (multiply 3/5 by 4 and 1/4 by 5 to have common denominators)
Make These Into a Mixed Fraction
Subtract 112-65
Simplify (divide 47 into 20 how many times to get into a mixed fraction)
I think this is right. Hope This Helps