(England, Wales, Non-
UK 8 (60
minutes)
In the diagram, PQRS, JQK and LRK are straight lines
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Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Question 7
Question 8
Question 9
Question 10
Question 11
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33°
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270/R
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Question 12
Question 13
What is the size of the angle JKL?

∠JKL = 38°

Step-by-step explanation:

PQRS, JQK and LRK are straight lines

Let's take the straight lines in the diagrams one after the other to find what they consist.

The related diagram can be found at (question ID: 18713345)

Find attached the diagram used for solving the question.

For straight line PQRS,

2x°+y°+x°+2y° = 180°

(Sum of angles on a Straight line = 180°)

Collect like terms

3x° + 3y° = 180°

Also straight line PQRS = straight line PQR + straight line SRQ

For straight line PQR,

2y + x + ∠RQM = 180° ....equation 1

For straight line SRQ,

2x + y + ∠MRQ = 180° ....equation 2

Straight line PQRS = addition of equation 1 and 2

By collecting like times

3x +3y + ∠RQM + ∠MRQ = 360°....equation 3

Given ∠QMR = 33°

∠RQM + ∠MRQ + ∠QMR = 180° (sum of angles in a triangle)

∠RQM + ∠MRQ + 33° = 180°

∠RQM + ∠MRQ = 180-33

∠RQM + ∠MRQ = 147° ...equation 4

Insert equation 4 in 3

3x° +3y° + 147° = 360°

3x +3y = 360 - 147

3x +3y = 213

3(x+y) = 3(71)

x+y = 71°

∠JQP = ∠RQK = 2y° (vertical angles are equal)

∠LRS = ∠QRK = 2x° (vertical angles are equal)

∠QRK + ∠RQK + ∠QKR = 180° (sum of angles in a triangle)

2x+2y + ∠QKR = 180

2(x+y) + ∠QKR = 180

2(71) + ∠QKR = 180

142 + ∠QKR = 180

∠QKR = 180 - 142

∠QKR = 38°

∠JKL = ∠QKR = 38°

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

yes.. it's proven to be 36.