# Lesson: Lines and Angles

## Comment on Lines and Angles

### knowledgeble video

knowledgeble video
very nice﻿

### At 1:40 in the video how do

At 1:40 in the video how do you know that the line is a straight line (and not bent)? ### On the GRE, a line that

On the GRE, a line that appears to be straight can assumed to be straight. For more on what can and cannot be assumed with GRE Geometry diagrams, see this video: https://www.greenlighttestprep.com/module/gre-geometry/video/863

### Hey ! I really did not

Hey ! I really did not understand the GRE practice question ( 160 to 170 difficulty level) after r/(r+s)=r/180 ( I didn't understand this part at all) , would you mind explaining it to me again ? is there any other way to approach the problem ? ### You're referring to this

You're referring to this question: http://greprepclub.com/forum/in-the-figure-above-if-what-is-the-value-of...

We're told that r/(r+s) = 5/8

On the diagram, we see that angle r and angle s both lie on the same line, which means they must add to 180 degrees. In other words, r+s = 180

So, we can take the given information, r/(r+s) = 5/8, and replace (r+s) with 180 to get: r/180 = 5/8

To solve this, we can first cross multiply the fractions.
We get: (8)(r) = (5)(180)
Or: 8r = 900
Divide both sides by 8 to get: r = 900/8 = 112.5

Does that help?

### Very easy to comprehend tanxs

Very easy to comprehend tanxs for all your tutorials online you are a good instructor. Thanks!

### Please let me know that what

Please let me know that what all sections are need to be practiced from Khan academy. ### Sure thing!

Sure thing!

Keep in mind that these links are for reinforcement, so you need not answer all of the questions in the Khan Academy links. That said, they're great for extra practice.

Cheers,
Brent

### Hello, I have a question

Hello, I have a question regarding ETS question in the 3rd edition:

-116(4): it clearly states that PQ=PR are equal then how can the answer be D? Please kindly explain why C can't be an answer.

-280 (3): don't know why the answer is z=x+y. There is no indication that line x and y are equal ....

-280 (5): I don't know how to solve this problem. Need your kind guidelines.

-281(8): similar to to above question. Need your kind instructions

Thank you very much ### Hi jenibae.

Hi jenibae.

Page 116, question 4: Sandy provides a nice solution here: https://greprepclub.com/forum/pq-pr-3119.html#p6295
(let me know if you'd like me to elaborate on any steps.

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Page 280, question 3: In the triangle, we have two angles: one is x degrees, and the other is y degrees.
Let's let Q represent the 3rd (unlabeled) angle in the triangle.

Since all 3 angles must add to 180 degrees, we know that x + y + Q = 180 degrees.
So, Q = 180 - x - y

Alternatively, since angle Q and angle z are on the same line we know that z + Q = 180 degrees.
Solve this equation for Q to get: Q = 180 - z

We now have two equations: Q = 180 - x - y and Q = 180 - z

Since both equations are set equal to Q, we can write: 180 - x - y = 180 - z
Subtract 180 from both sides to get: -x - y = -z
Multiply both sides by -1 to get: x + y = z

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Page 280, question 5: In a regular decagon (10-sided polygon), all 10 angles are EQUAL.

Useful rule: The sum of the angles in an n-sided polygon = (n - 2)(180 degrees)

So, the sum of the angles in an 10-sided polygon = (10 - 2)(180 degrees)
= 1440 degrees

If each angle is equal, then the measurement of each angle = 1440/10 = 144 degrees

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Page 281, question 8:
∆NOP is SIMILAR to the smaller triangle in the diagram.
So, the ratios of their CORRESPONDING sides must be equal.
So, we get: 50/40 = NO/24
Solve to get: side NO = 30

Once we know that side NO = 30, we can use the Pythagorean Theorem to determine the length of side OP
Let x = length of side OP
We can write: 30² + 50² = x²
Evaluate: 900 + 2500 = x²
Simplify: 3400 = x²
So, x = √3400
= (√100)(√34)
= 10√34
RELATED VIDEO: https://www.greenlighttestprep.com/module/gre-geometry/video/872

### https://greprepclub.com/forum

https://greprepclub.com/forum/in-the-figure-above-line-k-is-parallel-to-line-m-1871.html

According to video, this is a parallel line and Angeles on line added to 180 " 2y+ 35 = 180 then y = 42.5. But, the given answer is " 2y = 35 then y= 17.5" which is seems applied opposite Angeles equality rules.

This is highly appreciated if you could explain why this one " 2y+ 35 = 180 " not working and provide us a different result? 