GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Dec 2018, 12:36

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Prep Hour

December 11, 2018

December 11, 2018

09:00 PM EST

10:00 PM EST

Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
• ### The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# In the trapezoid above, BC is parallel to AD, angle A is 45 degrees

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 26 Dec 2015
Posts: 258
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
In the trapezoid above, BC is parallel to AD, angle A is 45 degrees  [#permalink]

### Show Tags

20 Feb 2018, 19:45
1
1
00:00

Difficulty:

65% (hard)

Question Stats:

52% (02:25) correct 48% (02:35) wrong based on 44 sessions

### HideShow timer Statistics

In the trapezoid above, BC is parallel to AD, angle A is 45 degrees and the length of line segment CD is 20. If the height of the trapezoid is 10, then which of the following is the value of x+y?

A) 180

B) 255

C) 270

D) 285

E) 300

Attachments

E GEO.png [ 14.27 KiB | Viewed 523 times ]

BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 826
Location: India
GMAT 1: 710 Q49 V36
Re: In the trapezoid above, BC is parallel to AD, angle A is 45 degrees  [#permalink]

### Show Tags

20 Feb 2018, 20:58
1
LakerFan24 wrote:
In the trapezoid above, BC is parallel to AD, angle A is 45 degrees and the length of line segment CD is 20. If the height of the trapezoid is 10, then which of the following is the value of x+y?

A) 180

B) 255

C) 270

D) 285

E) 300

given cd = 20

hieght is 10 , we have a right angle triangle.. hypotunese 20 side= 10

now we know side1^2 + side2^2 = hypotunese^2 ( pythagoras therom)

10^2 + x^2 = 20^2 i.e x^2 = 400 -100 = 300

X= rt300 = 10 rt 3

now sides are 10, 10rt3 and 20 ratio 1:rt3:2 .. the angles are 90-60-30

the smaller angle has the smaller side i.e angle D = 30

now x+y+ angle a + angle b = 360 ( angle in a quadilateral)

x+y = 360 - a - b = 360 - 45 -30 =285

(D) imo
Director
Joined: 31 Jul 2017
Posts: 504
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
In the trapezoid above, BC is parallel to AD, angle A is 45 degrees  [#permalink]

### Show Tags

20 Feb 2018, 21:15
1
LakerFan24 wrote:
In the trapezoid above, BC is parallel to AD, angle A is 45 degrees and the length of line segment CD is 20. If the height of the trapezoid is 10, then which of the following is the value of x+y?

A) 180

B) 255

C) 270

D) 285

E) 300

We have -

$$X + A = 180$$. Given, $$A = 45 --> X = 135$$
$$Y + D = 180..... Y = 30$$ as Sin Y = $$\frac{10}{20}. Hence Y = 150$$
Hence, $$X + Y = 150 + 135 = 285$$
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Senior SC Moderator
Joined: 22 May 2016
Posts: 2201
In the trapezoid above, BC is parallel to AD, angle A is 45 degrees  [#permalink]

### Show Tags

22 Feb 2018, 20:02
LakerFan24 wrote:
In the trapezoid above, BC is parallel to AD, angle A is 45 degrees and the length of line segment CD is 20. If the height of the trapezoid is 10, then which of the following is the value of x+y?

A) 180

B) 255

C) 270

D) 285

E) 300

Attachment:

E GEO ed.png [ 16.23 KiB | Viewed 400 times ]

Find $$x$$:

A base angle and upper angle on the same side of a trapezoid sum to 180°
(Parallel lines cut by a transversal create supplementary adjacent interior angles.)
45 + x = 180
x = 135

Find y:
Drop an altitude from C to base AD at X.

∆ CDX is a right triangle
Trapezoid height = 10
For right ∆ CDX, Leg CX = 10
Hypotenuse CD = 20
Let Leg DX = $$L$$

$$L^2 + 10^2 = 20^2$$
$$L^2 = 300$$
$$\sqrt{L^2} =\sqrt{100*3}$$
$$L = DX= 10\sqrt{3}$$

If a right triangle has sides in ratio $$a : a\sqrt{3} : 2a$$,
angles opposite those sides, respectively, have measures 30°-60°-90°

$$10$$ corresponds with $$a$$
Leg CX must be opposite a 30° angle
$$10\sqrt{3}$$ corresponds with $$a\sqrt{3}$$.
Leg DX must be opposite a 60° angle

At vertex C, two angles form ∠$$y$$
∠XCD = 60
∠BCX = 90
$$y$$ = (90 + 60) = 150

$$x + y = (135 + 150) = 285$$

In the trapezoid above, BC is parallel to AD, angle A is 45 degrees &nbs [#permalink] 22 Feb 2018, 20:02
Display posts from previous: Sort by