Question

Abc is a triangle in wch 35 times the smallest angle is equal to the 26 times largest angle. what is the measure of the second largest angle (in degree)?

Answer 1

heya...!!!!!

let the

smaller angle be x
middle angle = y
larger angle = z

now,

35x = 26z

=> x = 26z/35

we know that:-

sum of all Angels of a triangle = 180°

26z/35 + y + z = 180°

=> y + (26z + 35z)/35= 180°

=> y + 61z/35 = 180°

=> y = ( 6300 - 61z)/35

the angles must be whole numbers, then z must be multiple of 35

if z = 35 then, y = (6300 - 61×35 )/35

=> y = ( 6300 - 2135)/35

=> y = 4165/35

=> y = 119 mid angle must be Less than 90

if z = 70 then, y = ( 6300 - 61 × 70)/35

=> y = (6300 - 4270)/35

=> y = 2030/35

=> y = 58 maybe this is the angle

let suppose another value of z

if z = 105 then, y = ( - 6300 61 × 105)/35

=> y = ( 6300 - 6405)/35

=> y = -105/35

=> y = -3 which is not possible

hence the middle angle y = 58

hope it's help you

Answer 2

Hi ,

Let the smallest angle = S

Largest angle = L

second largest angle = M

we know that ,

S + M + L = 180°

M = 180° - ( L + S ) ----( 1 )

according to the problem given ,

35S = 26L

S = 26L/35 ---( 2 )

L should be multiple of 35°

i ) if L = 35°

S = 26°

M = 180 - ( L + S )

= 180 - 61

= 119° > L

It is not possible.

ii ) if L = 70°

S = 52°

M = 180 - ( L + S )

= 180 - ( 70 + 52 )

= 180 - 122

= 58° ( possible )

iii ) if L = 105°

S = 78°

M = 180 - ( L + S )

= 180 - 183

= -3° ( not possible )

Therefore ,

second largest angle = M = 58°

I hope this helps you.

: )