Lines and Angles - Sample Questions

01
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Question 1.

Image 1.

In the above image,


If x-y=10, what is x?

 

02
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Answer 1.

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.

Image 1.

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

04
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Answer 2.

 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.

Image 1.

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

06
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Answer 3.

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

07
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Question 4.

Image 1.

 If   x / x-y  = 2, what is x?

08
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Answer 4.

 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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Answer 5.

Answer : 80:

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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Answer 6.

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

13
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Question 7.

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

14
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Answer 7.

Answer: 315.

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

15
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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?

16
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Answer 8.

B and D, A and E and D and E.
If A is complementary to B, then D ( vertical angle to A)  is also complementary to B. To follow this idea, if A is complementary to B, then  A is complementary to E (equal to B)
Finally, D and E must be complementary as D=A and E=B. 
Remember - complementary angles add up to 90o

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Your Citation
Russell, Deb. "Lines and Angles - Sample Questions." ThoughtCo, Aug. 29, 2016, thoughtco.com/lines-and-angles-sample-questions-2312319. Russell, Deb. (2016, August 29). Lines and Angles - Sample Questions. Retrieved from https://www.thoughtco.com/lines-and-angles-sample-questions-2312319 Russell, Deb. "Lines and Angles - Sample Questions." ThoughtCo. https://www.thoughtco.com/lines-and-angles-sample-questions-2312319 (accessed January 16, 2018).