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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.
The solution of y= given as:
x: 0 1 2 3
y: 0 3 10 21
<h3>What is Linear Equation?</h3>A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
Given function is:
y=
For finding the solution of above expression, take value of x and solve for y.
- If x=0
y= 2(0)+0
y=0
- If x=1,
y=
- If x=2
y=
- If x=3
y=
The required table is:
x: 0 1 2 3
y: 0 3 10 21
Learn more about linear equation here:
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