In triangle ABC, what is the measurement of angle C?

We know, the sum of the ∠A+∠B+∠C = 180
(1) The sum of the measurement of angles A and C is 120
substituting value of ∠A + ∠C - 120 ... 120+∠B = 180. We do not know what will be ∠C. ... Insufficient

A D / B C E

(2) The sum of the measurement of angles A and B is 80
substituting value of ∠A + ∠B - 80 ... 80+∠C = 180 .. ∠C=100 ... Sufficient

'B' is the winner

We are to determine angle C in triangle ABC.

Statement 1: The sum of the measurement of angles A and C is 120
From 1, we know that A+C=120. We can only determine angle B from the above statement, which is 180-120=60. A+C=120 leads to many possible values for angle C, hence statement 1 is insufficient.

Statement 2: The sum of the measurement of angles A and B is 80
Sufficient. We can determine C=180-(A+B)=180-80=100.

The answer is B.

angle a+b+c= 180
#1
The sum of the measurement of angles A and C is 120
insufficient
#2
The sum of the measurement of angles A and B is 80
so c= 100
sufficient
IMO B


In triangle ABC, what is the measurement of angle C?

(1) The sum of the measurement of angles A and C is 120
(2) The sum of the measurement of angles A and B is 80

(1) The sum of the measurement of angles A and C is 120 insufic

a+c+b=180, 120+b=180, b=60;

(2) The sum of the measurement of angles A and B is 80 sufic

a+c+b=180, 80+c=180, c=100.

Ans (B)

(1) The sum of the measurement of angles A and C is 120.
We only know that angle B is 60. We don't know the rest.
NOT SUFFICIENT

(2) The sum of the measurement of angles A and B is 80
We know that angle C is 100.
SUFFICIENT

FINAL ANSWER IS (B)

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In triangle ABC, what is the measurement of angle C?

(1) The sum of the measurement of angles A and C is 120
A + C = 120
and A + B + C = 180
Thus, B = 60
But nothing specific about angles A and C is available.

INSUFFICIENT.

(2) The sum of the measurement of angles A and B is 80
A + B = 80
A + B + C = 180
80 + C = 180
C = 100

SUFFICIENT.

Answer D.

In triangle ABC, what is the measurement of angle C?

(Statement1): The sum of the measurement of angles A and C is 120
--> It says nothing about whether the triangle is an equilateral triangle.
--> angle C could anything in the range from 1 to 120
Insufficient

(Statement2): The sum of the measurement of angles A and B is 80
--> <A+ <B+ <C=180
<A+ <B=80 --> <C= 100
Sufficient

The answer is B.

Two equations and 3 variables.....so insufficient....

OA:E

OFFICIAL EXPLANATION

1. Since the sum of the measure of the interior angles of a triangle equals 180 degrees, you can write the following equation:
The measure of angles A + B + C = 180

2. Evaluate Statement (1) alone.

Translate Statement (1) into algebra:
A + C = 120

Use the foundational triangle equation (i.e., all angles add up to 180):
A + B + C = 180
(A + C) + B = 180
Substitute A + C = 120 into the equation.
120 + B = 180
B = 60

It is impossible to determine the value of angle C. Angle A could be 60 degrees and angle C could be 60 degrees. However, angle A could be 20 degrees and angle C could be 100 degrees.

Statement (1) is NOT SUFFICIENT.

3. Evaluate Statement (2) alone.
Translate Statement (2) into algebra:
A + B = 80

Use the foundational triangle equation (i.e., all angles add up to 180):
A + B + C = 180
(A + B) + C = 180
Substitute A + B = 80 into the equation.
80 + C = 180
C = 100

Statement (2) is SUFFICIENT.

Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT, answer B is correct.