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# M70-13

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Math Expert
Joined: 02 Sep 2009
Posts: 59730

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03 Sep 2018, 03:50
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Difficulty:

45% (medium)

Question Stats:

29% (02:19) correct 71% (01:46) wrong based on 7 sessions

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If angle BDC is approximately 65°, what is the approximate value of x?

A. $$20$$
B. $$30$$
C. $$40$$
D. $$50$$
E. $$60$$

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Joined: 02 Sep 2009
Posts: 59730

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03 Sep 2018, 03:50
Official Solution:

If angle BDC is approximately 65°, what is the approximate value of x?

A. $$20$$
B. $$30$$
C. $$40$$
D. $$50$$
E. $$60$$

We’ll go for PRECISE because we have all the information we need to solve the question.

Adding AD and DC together, we see that triangle ABC is made up of lines of lengths 3, 4, 5 – a Pythagorean triplet! This means ∠B = 90°. Next, since BC = DC, we know that ∠CDB = ∠BDC = 65°. This makes ∠C = 180 – 65 – 65 = 50°. Now that we have two of the triangle’s angles, we can see that ∠A = 180 – 90 – 50 = 40°.

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Updated on: 02 Oct 2018, 01:59
1
This is a very poor quality question.

Originally posted by vb1991 on 01 Oct 2018, 14:34.
Last edited by vb1991 on 02 Oct 2018, 01:59, edited 1 time in total.
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01 Oct 2018, 14:45
1
x= Angle A= Sin-1(3/5)= 36.9 degrees.

But, by manipulating angles, we get 50 degrees.

There is an error in the question.

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01 Oct 2018, 22:29
vb1991 wrote:
This is a very poor quality question and the answer is wrong.

Since the larger triangle is a 3-4-5 type Pythagorean triangle with angle B = 90°, then the following HAS to be true:

angle A = 30°
angle C = 60°

vb1991

Mate, not all right angle triangles have measure of angles : 30, 60 and 90.

All right angled triangle will follow Pythagoras Theorem. But for 30-60-90 type right triangle sides will be in ratio : 1 : \sqrt{3} : 2

Clearly, 3-4-5 do not follow above side ratio.

So, angles will not be in 30-60-90 form for 3-4-5 right triangle.

In fact for 3-4-5 right triangle corresponding angles are 36.87 - 53.13 - 90.

Hope this helps!!
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02 Oct 2018, 02:01
Harshgmat wrote:
vb1991 wrote:
This is a very poor quality question and the answer is wrong.

Since the larger triangle is a 3-4-5 type Pythagorean triangle with angle B = 90°, then the following HAS to be true:

angle A = 30°
angle C = 60°

vb1991

Mate, not all right angle triangles have measure of angles : 30, 60 and 90.

All right angled triangle will follow Pythagoras Theorem. But for 30-60-90 type right triangle sides will be in ratio : 1 : \sqrt{3} : 2

Clearly, 3-4-5 do not follow above side ratio.

So, angles will not be in 30-60-90 form for 3-4-5 right triangle.

In fact for 3-4-5 right triangle corresponding angles are 36.87 - 53.13 - 90.

Hope this helps!!

I conflated two separate concepts, my bad. Thanks for the explanation!

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Joined: 21 Oct 2019
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01 Nov 2019, 11:11
Please explain how is ∠CDB = ∠BDC = 65°?
Re: M70-13   [#permalink] 01 Nov 2019, 11:11
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# M70-13

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