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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. \(60°\)
A. \(0°\)
B. \(15°\)
C. \(30°\)
D. \(40°\)
E. \(60°\)
02 Dec 2021, 03:52
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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
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
