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:
C. No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
Step-by-step explanation:
Dilation is the process in which the size i.e dimensions of a given figure is either increased or decreased by a scale factor, without changing the shape of the figure.
Given that: PA = 2, PB = 3, A
= 4, B
= 5.
So that: P = 6, P = 8.
Therefore, triangle A'B'C' is not an exact dilation of triangle ABC. So that the correct option is; No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
Answer:
Natalie have left with 5 beads.
Step-by-step explanation:
Given:
Natalie had 64 beads. She used 24 beads to make a bracelet. She used 7/8 of the remaining beads to make a necklace.
Now, to find the beads does Natalie have left.
<em>Total beads Natalie had = 64 beads.</em>
<em>And beads she used to make a bracelet = 24 beads</em>.
So, the remaining beads are = 
Now,<em> the beads she used to make a necklace</em> = 
= 
= 
= 
Hence, the beads Natalie have left = remaining beads - beads used to make necklace.
Therefore, Natalie have left with 5 beads.
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Answer:
51
Step-by-step explanation:
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