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:
For every 7 hair bands there will be 4 ribbons
7 hair bands →→ 4 ribbons
14 hair bands →→ 8 ribbons
21 hair bands →→ 12 ribbons
etc.
Answer:
= −11.2
Step-by-step explanation:
64.8=6(m+22)
We move all terms to the left:
64.8-(6(m+22))=0
We calculate terms in parentheses: -(6(m+22)), so:
6(m+22)
We multiply parentheses
6m+132
Back to the equation:
-(6m+132)
We get rid of parentheses
-6m-132+64.8=0
We add all the numbers together, and all the variables
-6m-67.2=0
We move all terms containing m to the left, all other terms to the right
-6m=67.2
Answer:
320 min. or 5 hrs 20 min.
Step-by-step explanation:
40 x 8 = 320