One of the angles of a triangle is 75°. If the difference of other two is 35°, then the largest angle of other two angles has a measure (a) 80° (b) 75° (c) 70° (d) 135°

Question

 I could not understand what they meant by "solving (I) and (ii)". Could you please tell me ?

Let the other two angles be x and y

Given x−y=35∘...........(i)

Now using the angle sum property of the triangle 

⇒x+y+75∘=180∘⇒x+y=105∘...........(ii)

Solving (i) and (ii)

x=70∘,y=35∘

So the measure of the largest angle is 75∘

Answer 1

let one angle be x then the other will be x+35                   (x+35-x=35)

x+x+35+75=180

2x+110=180

2x=180-110

2x=70

x=70/2

x=35

The other angle=x+35=35+35=70

Option (c) is the correct answer

The largest of the other two angles (35º,70º) is 70º

Another method (explanation of solving i and ii)

Method of elimination

Adding equations (i) and (ii)

 we have

2x=140

x=140/2

x=70

Substitute  x=70 in equation (i) or (ii) to find y

y=35

Hope you understand now.

Answer 2

i think it is right