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If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle

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If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle [#permalink]

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New post 05 Nov 2017, 02:06
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Question Stats:

81% (00:27) correct 19% (00:39) wrong based on 42 sessions

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If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle

(A) is isosceles
(B) is obtuse
(C) is a right triangle
(D) is equilateral
(E) has one angle greater than 80°
[Reveal] Spoiler: OA

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Re: If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle [#permalink]

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New post 05 Nov 2017, 02:17
Bunuel wrote:
If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle

(A) is isosceles
(B) is obtuse
(C) is a right triangle
(D) is equilateral
(E) has one angle greater than 80°


If the angles of the triangle are in the ratio 1:2:2,
and the sum of the angles in a triangle are 180, the three angles are 36,72,72 degree respectively.

Therefore, the triangle formed is isosceles because the sides opposite to equal angles are equal(Option A)
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If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle [#permalink]

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New post 05 Nov 2017, 13:20
Bunuel wrote:
If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle

(A) is isosceles
(B) is obtuse
(C) is a right triangle
(D) is equilateral
(E) has one angle greater than 80°

Angle ratio is 1 : 2 : 2 -->
x : 2x : 2x
Ratio parts' total = 5x

5x = 180 (degrees in a triangle)
x = 36

The three angle measures are
x = 36°
2x = (2)(36) = 72°, and
2x = (3)(36) = 72°

Sides opposite equal angles are equal. There are two equal sides opposite the 72° angles.
It is an isosceles triangle.

Answer A

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Re: If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle [#permalink]

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New post 05 Nov 2017, 19:28
Let the angles of triangle are x, 2x, 2x
x+2x+2x=180 (Sum of angles of triangle is \(180^{\circ}\))
5x= 180
x=\(\frac{180}{5}\)= \(36^{\circ}\)

other angles are 36*2= \(72^{\circ}\)

Sides opposite equal angles are equal. Thus, it is an isosceles triangle.

Answer: A.
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Re: If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle [#permalink]

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New post 06 Nov 2017, 10:43
Bunuel wrote:
If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle

(A) is isosceles
(B) is obtuse
(C) is a right triangle
(D) is equilateral
(E) has one angle greater than 80°



WITH THE RATIO, WE CAN DECIPHER THAT TWO ANGLES ARE EQUAL. SO THE TRIANGLE IS ISOSCELES TRAIANGLE.

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Re: If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle [#permalink]

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New post 12 Nov 2017, 08:34
Bunuel wrote:
If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle

(A) is isosceles
(B) is obtuse
(C) is a right triangle
(D) is equilateral
(E) has one angle greater than 80°


We can create the ratio:

x + 2x + 2x = 180

5x = 180

x = 36

Thus, our angles are 36, 72, and 72, so we have an isosceles triangle.

Answer: A
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Re: If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle [#permalink]

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New post 12 Nov 2017, 08:46
Bunuel wrote:
If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle

(A) is isosceles
(B) is obtuse
(C) is a right triangle
(D) is equilateral
(E) has one angle greater than 80°


An isosceles triangle is a triangle that has two sides of equal length and 2 equal angles, answer must be (A)
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Re: If the angles of a triangle are in the ratio 1 : 2 : 2, the triangle   [#permalink] 12 Nov 2017, 08:46
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