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In th triangle ABC, the measure of angle A is 25° and the m
[#permalink]
02 Feb 2017, 07:52

1

Expert Reply

Question Stats:

In the triangle ABC, the measure of angle A is 25° and the measure of angle B is greater than 90°. Which of the following could be the measure of angle C?

Indicate all such measures.

A) 12 degrees

B) 15 degrees

C) 45 degrees

D) 50 degrees

E) 70 degrees

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Joined: **07 Jun 2014 **

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Re: In th triangle ABC, the measure of angle A is 25° and the m
[#permalink]
12 Feb 2017, 15:34

1

Expert Reply

Explanation

SUPPLY a number for angle B. Since B > 90°, B can be anything greater than 90° (like 90.0009°), but start with the lowest possible integer, B = 91° to make calculations easier:

A + B + C = 180°

25° + 91° + C =180°

C = 64°

Now imagine if B were at the other extreme—as large as possible. :

A + B + C = 180°

25° + B + C =180°

B + C =155°

If B = 154°, then C = 1°

Angle C can be anything less than 65 degrees, so the first four answers are possible values of C.

Hence options A, B, C and D are correct.

di.jpg [ 10.21 KiB | Viewed 39606 times ]

di new.jpg [ 6.94 KiB | Viewed 38749 times ]

_________________

SUPPLY a number for angle B. Since B > 90°, B can be anything greater than 90° (like 90.0009°), but start with the lowest possible integer, B = 91° to make calculations easier:

A + B + C = 180°

25° + 91° + C =180°

C = 64°

Now imagine if B were at the other extreme—as large as possible. :

A + B + C = 180°

25° + B + C =180°

B + C =155°

If B = 154°, then C = 1°

Angle C can be anything less than 65 degrees, so the first four answers are possible values of C.

Hence options A, B, C and D are correct.

Show: :: Img

Attachment:

di.jpg [ 10.21 KiB | Viewed 39606 times ]

Attachment:

di new.jpg [ 6.94 KiB | Viewed 38749 times ]

_________________

Sandy

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Re: In th triangle ABC, the measure of angle A is 25° and the m
[#permalink]
23 Mar 2018, 11:03

Expert Reply

Absolutely. It is from the official software.

Regards

Regards

Re: In th triangle ABC, the measure of angle A is 25° and the m
[#permalink]
25 Mar 2018, 10:30

1

ejanlagreslayer wrote:

Sometimes I wonder if these kind of questions can be on the actual test

99,99%

Re: In th triangle ABC, the measure of angle A is 25° and the m
[#permalink]
05 Apr 2018, 02:30

3

since angle B is greater than 90; A+C<90 because sum of three angles of a traingle is 180.

so C<90-A==> C<65. options A,B,C,D satisfy this condition.

so C<90-A==> C<65. options A,B,C,D satisfy this condition.

Re: In th triangle ABC, the measure of angle A is 25° and the m
[#permalink]
24 May 2018, 09:51

1

Third angle < 180-(25+90)

Third angel < 65

Answer: A B C D

Third angel < 65

Answer: A B C D

Re: In th triangle ABC, the measure of angle A is 25° and the m
[#permalink]
13 Aug 2021, 15:35

1

In addition to the awesome answers provided, I might humbly add mine.

Process

1. B > 90, so as B gets greater, C gets smaller.

2. This means, when B is smallest, C is greatest. In this case, we'll cheat a little bit to ease calculations and treat B's "smallest" value as being 90 degrees.

3. So, for the sake of simplicity, let's assume that angle B is actually 90 degrees (it can't actually be 90 degrees by the parameters of the problem, but this will give us a figure to go forward from).

4. The internal angles of a triangle add up to 180 degrees. Therefore, 25 + 90 + C = 180.

5. That means that C = 65 in that example.

6. Since B will always be greater than 90, C will always be less than 65.

7. A, B, C, and D all fit the bill!

Cool tip:

The sum of the internal angles of any figure is equal to (n-2)*180 where n is the number of sides in the figure. This can be used when the problem involves figures other than a triangle.

Process

1. B > 90, so as B gets greater, C gets smaller.

2. This means, when B is smallest, C is greatest. In this case, we'll cheat a little bit to ease calculations and treat B's "smallest" value as being 90 degrees.

3. So, for the sake of simplicity, let's assume that angle B is actually 90 degrees (it can't actually be 90 degrees by the parameters of the problem, but this will give us a figure to go forward from).

4. The internal angles of a triangle add up to 180 degrees. Therefore, 25 + 90 + C = 180.

5. That means that C = 65 in that example.

6. Since B will always be greater than 90, C will always be less than 65.

7. A, B, C, and D all fit the bill!

Cool tip:

The sum of the internal angles of any figure is equal to (n-2)*180 where n is the number of sides in the figure. This can be used when the problem involves figures other than a triangle.

gmatclubot

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