Can we solve this triangle with the given information?

[mcheytan]

The question gives some information. At the end, there are two pieces of information that are provided. The question is: "which piece of information is necessary to answer the question (with yes or no).

In the Isoceles triangle RST, what is angle R
1)Angle T=100 degrees
2)Angle S=40 degrees

It can be
a) only 1) alone is sufficient, but not 2)
b) only 2) alone is sufficient, but not 1)
c) 1) and 2) TOGETHER are necessary to solve it
d) NEITHER is sufficient
e) 1) and 2) INDIVIDUALLY are sufficient

Shouldn't it be e), because it does not matter which angle we are given, since we have two identical angles we can find out by subtracting from 180 and/or dividing by 2????

The answer is a)!!!!

 

[Mrspi]

Re: Can we solve this with ...

The question gives some information. At the end, there are two pieces of information that are provided. The question is: "which piece of information is necessary to answer the question (with yes or no).

In the Isoceles triangle RST, what is angle R
1)Angle T=100 degrees
2)Angle S=40 degrees

It can be
a) only 1) alone is sufficient, but not 2)
b) only 2) alone is sufficient, but not 1)
c) 1) and 2) TOGETHER are necessary to solve it
d) NEITHER is sufficient
e) 1) and 2) INDIVIDUALLY are sufficient

Shouldn't it be e), because it does not matter which angle we are given, since we have two identical angles we can find out by subtracting from 180 and/or dividing by 2????

The answer is a)!!!!

You are told that triangle RTS is isosceles, but you are not told which two sides are equal.

Knowing that m<S = 40 is not sufficient to solve the problem, because <S could be the vertex angle (in which case <R and <T would each have measures of 50), or <S could be one of the equal base angles, (in which case the other base angle would have a measure of 40....but we don't know whether that other base angle is R or T!....) So, 2) alone is not sufficient information to solve the problem.

Now, can you think about WHY 1) alone IS sufficient?

 

[mcheytan]

Re: Can we solve this with ...

Ohh yes! I feel stupid now....and I used to adore math.... :shock:

 

[soroban]

Hello, mcheytan!

Did you make any sketches?

The question gives some information.
At the end, there are two pieces of information that are provided.
The question is: "Which piece of information is necessary to answer the question (with yes or no) ?".

In the Isoceles triangle RST, what is angle R?

. . \(\displaystyle [1]\;\;\angle T\:=\:100^o\)
. . \(\displaystyle [2]\;\;\angle S\:=\:40^o\)

It can be:

. . \(\displaystyle \begin{array}{cc} (a) & \text{[1] is sufficient, but not [2]} \\ (b) & \text{[2] is sufficient but not [1]} \\ (c) & \text{both [1] and [2] are necessary} \\ (d) & \text{neither is sufficient} \\ (e) & \text{[1] and [2] individually are sufficient} \end{array}\)

\(\displaystyle \text{If [1] }\angle T \,=\,100^o\text{, we know that T cannot be a base angle.}\)
. . \(\displaystyle \text{(The triangle would have two 100-degree angles!)}\)
\(\displaystyle \text{Hence: }T = 100^o\text{ is the vertex angle, and the base angles are }40^o\text{ each.}\)
. . \(\displaystyle \text{Therefore: }\:\angle R \:=\:40^o\)


\(\displaystyle \text{If [2] }\angle S = 40^o\text{, then S could be the vertex angle.}\)
. . \(\displaystyle \text{Hence: }\:\angle R \:=\:\angle T \:=\:70^o\)
\(\displaystyle \text{But }\angle S = 40^o\text{ could be a base angle.}\)
. . \(\displaystyle \text{If R is a base angle: }\,R \:=\:40^o\)
. . \(\displaystyle \text{If R is the vertex angle: }\,R \:=\:100^o\)

\(\displaystyle \text{With [2], there are }three\text{ possible values for angle R.}\)


\(\displaystyle \text{Therefore: }\;\text{(a) [1] is sufficient, but not [2]}\)

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By the way, just how do I answer the question?

"What is angle R?"

. . Um . . . Yes?