Abhi077 wrote:
Attachment:
GC2.png
If AB < BC < CA, AD = DC, and each angle of triangle ACB is a whole number of degrees, which of the following is the maximum possible value of angle DAB? (Note: Diagram is not drawn to scale)
A) 9°
B) 14°
C) 19°
D) 21°
E) 51°
We have AB < BC < CA
In a triangle angle opposite to largest side has highest value and the one corresponding to smallest side has lowest value, therefore
Angle ACB < Angle BAC < Angle CBA
=> 51° < 50°+x < Angle CBA
(using sum of angles of triangle = 180°)
=> 51° < 50°+x < 180°- 51°- (50°-x)
=> 51° < 50°+x < 79°- x
To find highest value of x,
50°+x < 79°- x
=> 2x < 79°- 50°
=> x < 29°/2
=> x < 14.5°
As all angles are whole numbers, highest value of x is 14°
Answer choice (B)
Posted from my mobile device