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The leftmost triangle has two angles labeled 40° and 70° [#permalink]
Expert's post 00:00

Question Stats: 72% (01:19) correct 27% (01:11) wrong based on 11 sessions

Attachment: triangles.jpg [ 36.21 KiB | Viewed 1584 times ]

 Quantity A Quantity B X 6

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The leftmost triangle has two angles labeled 40° and 70° [#permalink]
how can we solve this?
Founder  Joined: 18 Apr 2015
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Kudos [?]: 2036 , given: 8089

Re: The leftmost triangle has two angles labeled 40° and 70° [#permalink]
Expert's post
OE

Quote:
The leftmost triangle has two angles labeled 40° and 70°. Subtract these from 180° (the sum of the angles in any triangle) to determine that the third angle is 70°. Subtract 130 – 70 = 60° to get the measure of the adjoining angle in the rightmost triangle. Since the leftmost triangle is isosceles, the two long sides are each equal to 10. Since the rightmost triangle is a 30–60–90 triangle, the sides are in the proportion $$x: \sqrt{3} x : 2x$$

Because the hypotenuse is 8 and also the 2x in the ratio, the shortest leg of this triangle is x = 4. To calculate x, subtract: 10 – 4 = 6. The two quantities are equal.

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Re: The leftmost triangle has two angles labeled 40° and 70° [#permalink]
Carcass wrote:

 Quantity A Quantity B X 6

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Now consider the triangle ABC(diag. attached)

We have

angle B = 70 and angle A = 40

Therefore angle C = 70 (180-(40+70)).

Since angle b = angle c

therefore side AB= side AC = 10.

Now consider the triangle GFC

angle G = 90, and angle C in this triangle = 60 (130 -70 , in triangle ABC, angle C= 70)

and angle F = 30 (180 - (90+60)). NOw we have a 30-60-90 triangle.

Side CF = 8, therefore by 30-60-90 triangle properties ( sides distribute in the ratio = 1:$$\sqrt{3}$$ :2)

We have GF = $$4\sqrt{3}$$ and GC = 4.

Now to find AG, we know

AG = AC- GC

or AG = 10 -4 = 6.
Attachments triangles.jpg [ 23.69 KiB | Viewed 1481 times ]

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GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests Re: The leftmost triangle has two angles labeled 40° and 70°   [#permalink] 27 Sep 2017, 21:32
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