In isosceles triangle ABC, the degree measure of angle ABC is 30°, wha

Question

GMAT Club Tests' Fresh Question:

In isosceles triangle ABC, the degree measure of angle ABC is 40°. What is the difference between the maximum possible degree measure of the largest angle in the triangle ABC and the minimum possible degree measure of the largest angle in the triangle ABC?

A) 0°
B) 15°
C) 30°
D) 40°
E) 60°

M37-78

Bunuel · Accepted Answer

Official Solution:

In isosceles triangle ABC, the degree measure of angle ABC is  40° . What is the difference between the maximum possible degree measure of the largest angle in the triangle ABC and the minimum possible degree measure of the largest angle in the triangle ABC?

A.  0° 
B.  15° 
C.  30° 
D.  40° 
E.  60°

In isosceles triangle, two angles are equal to each other. 
 
If equal angles are  40° , then the third angle will be  180° - (40°+40°)=100° . So, in this case the angles are  40°, \ 40°, \ 100° .
 
If equal angles are  x° , then  x=\frac{180° - 40°}{2}=70° . So, in this case the angles are  40°, \ 70°, \ 70° .
 
The maximum possible degree measure of the largest angle is therefore  100° , and the minimum possible degree measure of the largest angle is  70° . 
 
The difference is  100°-70°=30° .

Answer: C

Abhishek009 · Answer

40° can either be the base angle / the apex angle

If 40° is base angles then Apex angle is 100° , thus difference will be 60° 
If 40° is Apex angle then Base angles are 70° , thus difference will be 30°

Thus, he minimum possible degree measure of the largest angle in the triangle ABC will be C) 30°

EgmatQuantExpert · Answer

Solution

Given:  
• In isosceles triangle ABD, the degree measure of angle ABC is 40°

To find:  
• The difference between the maximum possible degree measure of the largest angle in the triangle ABC and the minimum possible degree measure of the largest angle in the triangle ABC

Approach and Working:   
As there is no details provided about the angle ABC except the value, we can have 2 possible cases.

Case 1: 
If angle ABC is one of the same angle in the base, then the 3 angles of triangle ABC are 40°, 40°, and 100°
 • Largest angle = 100°

Case 2: 
If angle ABC is the vertex angle, then the 3 angles of triangle ABC are 40°, 70°, and 70°
 • Largest angle = 70°

Therefore the difference between the maximum largest angle and minimum largest angle = maximum possible largest angle – minimum possible largest angle = 100° - 70° = 30°

Hence, the correct answer is option C.

Answer: C

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

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In isosceles triangle ABC, the degree measure of angle ABC is 30°, wha

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