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In the figure, what is the value of x?

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In the figure, what is the value of x?  [#permalink]

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New post 21 Jun 2017, 00:08
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A
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In the figure, what is the value of x?

(A) 20˚
(B) 30˚
(C) 40˚
(D) 50˚
(E) 60˚


Attachment:
2017-06-21_1205.png
2017-06-21_1205.png [ 10.24 KiB | Viewed 4516 times ]

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Re: In the figure, what is the value of x?  [#permalink]

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New post 21 Jun 2017, 00:19
1
sum of all angles in a triangle is 180

hence x = 180 - (50+40+40)

answer is 50
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Re: In the figure, what is the value of x?  [#permalink]

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New post 21 Jun 2017, 00:35
Bunuel wrote:
Image
In the figure, what is the value of x?

(A) 20˚
(B) 30˚
(C) 40˚
(D) 50˚
(E) 60˚
Attachment:
2017-06-21_1205.png


Angle ABC = 40 + 40 = 80
Since the sum of angles in a triangle equals = 180,
Angle ACB = 180 - 80 - 50 = 50

Hence Answer D
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Re: In the figure, what is the value of x?  [#permalink]

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New post 21 Jun 2017, 00:39
Angle D(angle on a straight line) = 180˚

Consider Triangle ADB(the sum of the angles is 180˚)
Given Angle A = 50˚, Angle B = 40˚
Angles A + B + ADB = 180˚

Therefore Angle ADB = 180˚- (40˚+50˚) = 90˚

Now, Angle BDC = 180˚ - ADB = 90˚

Consider Triangle BDC(the sum of angles is 180˚)
Angles BDC + DBC + DCB = 180˚
Angle x = 180˚ - (90˚ + 40˚) = 50˚(Option D)
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Re: In the figure, what is the value of x?  [#permalink]

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New post 21 Jun 2017, 03:13
ADB = 180-(50+40) = 90
BDC= 180-ADB = 180-90 = 90
x = 180-(90+40) = 50
Ans D
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  [#permalink]

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New post 21 Jun 2017, 09:24
D.

In Triangle CDB
Angle D = 90 and Angle B =40
X = 180 - 130 = 50

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Re: In the figure, what is the value of x?  [#permalink]

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New post 22 Jun 2017, 02:04
Bunuel wrote:
Image
In the figure, what is the value of x?

(A) 20˚
(B) 30˚
(C) 40˚
(D) 50˚
(E) 60˚


Attachment:
2017-06-21_1205.png


In a triangle Exterior angle = Sum of opposite interior angles
-> /_BDC = /_DBA + /_BAD
-> /_BDC = 40 + 50 = 90

In triangle BDC ,
/_BDC + /_DCB + /_CBD = 180
-> 90 + x + 40 = 180
-> x = 50

Answer D
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Re: In the figure, what is the value of x?  [#permalink]

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New post 24 Jun 2017, 07:37
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Bunuel wrote:
Image
In the figure, what is the value of x?

(A) 20˚
(B) 30˚
(C) 40˚
(D) 50˚
(E) 60˚


The sum of all angles in any triangle is 180 degrees. Looking at our diagram, we see that angle ADB in triangle ADB must be 180 - 90 = 90 degrees.

The measure of a straight angle, such as AC, is 180 degrees. Since angle ADB is 90 degrees, we see that angle BDC must also equal 90 degrees.

Since x is the measure of angle C in triangle BDC with angle BDC = 90 degrees and angle DBC = 40 degrees, angle DCB = x = 180 - (40 + 90) = 50 degrees.

Alternate Solution:

Looking at the greater triangle ABC, we see that two of the interior angles are 50 and 40 + 40 = 80. Thus, the third interior angle, x, will be 180 - 50 - 80 = 50.

Answer: D
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Re: In the figure, what is the value of x?  [#permalink]

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New post 24 Jun 2017, 08:34
50+40+40+x=180
so x=50
hence D
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In the figure, what is the value of x?  [#permalink]

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New post 25 Jun 2017, 07:19
Bunuel wrote:
Image
In the figure, what is the value of x?

(A) 20˚
(B) 30˚
(C) 40˚
(D) 50˚
(E) 60˚
Attachment:
2017-06-21_1205.png

Solving with the larger triangle ABC is probably faster.

You could also use ASA: for two triangles, if any two angles and their included side are equal, the triangles are congruent.

Triangles here share side BD, and ∠ABD = ∠CBD = 40°.

They also have equal angles of 90°: ∠ADB (derived from what must be third angle of triangle ABD) and ∠BDC (because it lies, with ∠ADB, on straight line of 180°).

Side BD is "included" between the 40° and 90° angles in both triangles. ∠A = 50. ∠C (x) must also = 50. Answer D
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Re: In the figure, what is the value of x?  [#permalink]

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New post 26 Jun 2017, 23:23
50 + 40 + 40 + x = 180
x = 50
Ans D

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Re: In the figure, what is the value of x?  [#permalink]

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New post 26 Jun 2017, 23:38
Bunuel wrote:
Image
In the figure, what is the value of x?

(A) 20˚
(B) 30˚
(C) 40˚
(D) 50˚
(E) 60˚


Attachment:
2017-06-21_1205.png


Sum of the Angles of \(\triangle ABC = 180˚\)

\(\angle ABC + \angle BCA + \angle CAB = 180˚\)

Given \(\angle CAB = 50˚\)

Given \(\angle ABC = 40˚ + 40˚ = 80˚\)

Given \(\angle BCA = x\)

\(80˚ + x + 50˚ = 180˚\)

\(130˚ + x = 180˚\)

\(x = 180˚ - 130˚ = 50˚\) . Answer (D)...
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Re: In the figure, what is the value of x?  [#permalink]

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New post 10 Sep 2018, 07:07
Bunuel wrote:
Image
In the figure, what is the value of x?

(A) 20˚
(B) 30˚
(C) 40˚
(D) 50˚
(E) 60˚


Attachment:
2017-06-21_1205.png


Clean (D) \(180 - ( 50 + 40 +40) = 50˚\)
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