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In the figure, what is the value of x?
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21 Jun 2017, 00:08
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Re: In the figure, what is the value of x?
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21 Jun 2017, 00:19
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?
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21 Jun 2017, 00:35
Bunuel wrote: In the figure, what is the value of x? (A) 20˚ (B) 30˚ (C) 40˚ (D) 50˚ (E) 60˚ Attachment: 20170621_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?
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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?
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21 Jun 2017, 03:13
ADB = 180(50+40) = 90 BDC= 180ADB = 18090 = 90 x = 180(90+40) = 50 Ans D



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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?
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22 Jun 2017, 02:04
Bunuel wrote: In the figure, what is the value of x? (A) 20˚ (B) 30˚ (C) 40˚ (D) 50˚ (E) 60˚ Attachment: 20170621_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?
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24 Jun 2017, 07:37
Bunuel wrote: 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?
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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?
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25 Jun 2017, 07:19
Bunuel wrote: In the figure, what is the value of x? (A) 20˚ (B) 30˚ (C) 40˚ (D) 50˚ (E) 60˚ Attachment: 20170621_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?
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26 Jun 2017, 23:23
50 + 40 + 40 + x = 180 x = 50 Ans D Sent from my Redmi Note 3 using GMAT Club Forum mobile app



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Re: In the figure, what is the value of x?
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26 Jun 2017, 23:38
Bunuel wrote: In the figure, what is the value of x? (A) 20˚ (B) 30˚ (C) 40˚ (D) 50˚ (E) 60˚ Attachment: 20170621_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?
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10 Sep 2018, 07:07
Bunuel wrote: In the figure, what is the value of x? (A) 20˚ (B) 30˚ (C) 40˚ (D) 50˚ (E) 60˚ Attachment: 20170621_1205.png Clean (D) \(180  ( 50 + 40 +40) = 50˚\)
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