# Lines and Angles - Sample Questions

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### Question 1.

In the above image,

If x-y=10, what is x?

02
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We know that x + y = 180 as any acute angle formed by a transversal that cuts across 2 parallel line is supplementary. So with this in mind we can create 2 equations with 2 variables.

x + y = 180
x - y =   10
------------------
2x = 190
x = 95

03
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### Question 2.

Consider the image above, If the ratio of x to y is 6:4, what is y?

04
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Setup a ratio using an unknown multiplier, ?.
x/y = 6? / 4?
x + y = 180 = 6? + 4? = 10?
180 = 10?
? = 18
y = 4(18)
y = 72

05
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### Question 3.

See image 1 above.
if x + (x + y) = 320, what is x?

06
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Using  x + y =180 we can create 2 equations.
-x - y = -180
2x + y = 320
-------------------
x = 140

07
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### Question 4.

If   x / x-y  = 2, what is x?

08
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Using x + y = 180
x
-------   = 2
x - y
or x - 2y = 0
-  x + y = 180
----------------------
-3y = -180

y = 60  therefore
x + 60 = 180

x = 120

09
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### Question 5.

Refer to image above.
If A= 80, what is B +D - E?

10
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We know that A and D are vertical angles so they have the same measurement. ( 80)
F and C are also vertical angles, as are B and E.
So B + D - E means that B and -E = 0 as they are the same measurement. That leaves only D, which is = A = 80.

11
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### Question 6.

See image above.
If C + F = 80 and D= 80,  what is B?

12
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C and F are vertical angles so they are the same. The sum of the two = 80, so
C and F must  each be 80/2 = 40.
We know that D = 80.
We know that angle DCB forms a straight line = 180.
So D (80) + C (40) + B = 180
B = 180-80-40
B = 60

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### Question 7.

If e -=45, what is the sum of all other angles?

14
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All the angles form a circle, which is 360.
Subtract 45 from 360 we get  315.

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### Question 8.

If A and B are complementary angles (sum to 90), name three other pairs of angles
that  are complementary?

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