Question

The largest angle of a triangle is equal to the sum of the other two angles. The smallest angle is 1/4 of the largest angle. Find the angles of the triangle.

Please answer this fast!! Preferably by a meritnation expert.. :)

Answer 1

Let the largest angle be 'a' and smallest be 'c'
a+b+c = 180 [sum property of angles of a traingle]
Given, a =  (b+c)
c = 1/4 a
a = b + a/4
a - a/4 = b
b = 3a/4
a + 3a/4 + a/4 = 180
a + a = 180
2a = 180
a = 90
b = 3a/4 = 67.5 
c = a/4 = 22.5
Hence angles are 90 , 67.5 , 22.5
Hope it helps.

Answer 2

Answer:

Step-by-step ∠A be the largest angle

∠A+∠B+∠C= 180° (angle sum prop.)

A/q

∠A=1/4∠c

∠B=4∠A+∠A/4

∠B=3/4∠A

∠A+∠B+∠C= 180°

∠A+3/4∠A+1/4∠A= 180°

4∠A+3∠A+∠A/4=180°

8∠A= 180×4

∠A=180×4/8

∠A=90°

∴ ∠B=3/4×90

        =67.5

∠C=1/4×90

     = 22.5

∴∠A=90°,∠B=67.5°&∠C=22.5°: