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Find the value of X in the given quadrilateral.

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Find the value of X in the given quadrilateral.  [#permalink]

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New post 06 Oct 2018, 10:05
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Question Stats:

56% (01:55) correct 44% (01:29) wrong based on 57 sessions

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Find the value of X in the given quadrilateral.


A. 60 degrees.

B. Greater than 60 degrees.

C. Less than 60 degrees.

D. 90 degrees.

E. Can't be determined.


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Find the value of X in the given quadrilateral.  [#permalink]

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New post 06 Oct 2018, 19:05
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Arun1994 wrote:
Find the value of X in the given quadrilateral.

A. 60 degrees.
B. Greater than 60 degrees.
C. Less than 60 degrees.
D. 90 degrees.
E. Can't be determined.

Attachment:
anglex10.06.18.jpg
anglex10.06.18.jpg [ 32.07 KiB | Viewed 448 times ]

This question tests equilateral triangles, the triangle inequality theorem,
and the relationship between sides and angles in a triangle.

Draw a line that connects vertex A (on the diagram) to vertex C.
The larger triangle, ABC, has two equal sides.
Having seen answer choices, ask: can x = 60° or 90°?

Can x = 60°?
By definition of an equilateral triangle, if AC = 10, then x = 60°
x can = 60° if ∆ ABC is equilateral*
∆ ABC is equilateral only if AC = 10

Can side AC = 10?

Now consider ∆ ACD
Triangle inequality theorem:
The third side of a triangle should be greater than the difference between the other two sides and
less than the sum of the other two sides. So:
(9-1) < AC < (9+1)
8 < AC < 10
AC cannot = 10
AC must be less than 10

If AC must be less than 10, then
x must be less than 60°
If the length of a side of a triangle decreases, the angle measure opposite that side decreases, too.

The sides that are opposite the y angles both = 10
(AB and BC = 10)
ONLY if AC = 10, then x = 60°

AC must be less than 10. Therefore
x must be less than 60°

Answer C


* Or plug in.
If x = 60, then the other two angles, y, must also each be 60°
x + 2y = 180°
60 + 2y = 180
2y = 120
y = 60

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Find the value of X in the given quadrilateral.   [#permalink] 06 Oct 2018, 19:05
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