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In the figure, what is the value of x?

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Joined: 02 Sep 2009
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In the figure, what is the value of x?  [#permalink]

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21 Jun 2017, 01:08
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5% (low)

Question Stats:

93% (00:22) correct 7% (00:16) wrong based on 128 sessions

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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 [ 10.24 KiB | Viewed 5051 times ]

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

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21 Jun 2017, 01:19
1
sum of all angles in a triangle is 180

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

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

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21 Jun 2017, 01:35
Bunuel wrote:

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

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

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21 Jun 2017, 01:39
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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21 Jun 2017, 04:13
BDC= 180-ADB = 180-90 = 90
x = 180-(90+40) = 50
Ans D
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21 Jun 2017, 10:24
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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22 Jun 2017, 03:04
Bunuel wrote:

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

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

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24 Jun 2017, 08:37
1
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.

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

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24 Jun 2017, 09:34
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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25 Jun 2017, 08:19
Bunuel wrote:

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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27 Jun 2017, 00:23
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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27 Jun 2017, 00:38
Bunuel wrote:

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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10 Sep 2018, 08:07
Bunuel wrote:

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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Re: In the figure, what is the value of x?   [#permalink] 10 Sep 2018, 08:07
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