Question

Each set of numbers below represents the measures of three angles. Which set represent angle measures that could be found in a triangle? A(30o, 40o, 30o) B(42o, 18o, 130o) C(10o, 15o, 100o) D(40o, 5o, 40o) E (60o, 45o, 75o) F (20o, 40o, 50o)

Answer 1

Option E -
`(60^\circ, 45^\circ, 75^\circ)`

Explanation:

Given : Each set of numbers below represents the measures of three angles.

To find : Which set represent angle measures that could be found in a triangle?

Solution :

We know that,

Sum of all three angles of triangle is 180°.

So whose sum is 180° that pair form a triangle.

A)
`(30^\circ, 40^\circ, 30^\circ)`

Sum of angles,

`30^\circ+40^\circ+30^\circ=100^\circ`

No, this set is not a triangle.

B)
`(42^\circ, 18^\circ, 130^\circ)`

Sum of angles,

`42^\circ+18^\circ+130^\circ=190^\circ`

No, this set is not a triangle.

C)
`(10^\circ, 15^\circ, 100^\circ)`

Sum of angles,

`10^\circ+15^\circ+100^\circ=125^\circ`

No, this set is not a triangle.

D)
`(40^\circ, 5^\circ, 40^\circ)`

Sum of angles,

`40^\circ+5^\circ+40^\circ=85^\circ`

No, this set is not a triangle.

E)
`(60^\circ, 45^\circ, 75^\circ)`

Sum of angles,

`60^\circ+45^\circ+75^\circ=180^\circ`

Yes, this set is a triangle.

F)
`(20^\circ, 40^\circ, 50^\circ)`

Sum of angles,

`20^\circ+40^\circ+50^\circ=110^\circ`

No, this set is not a triangle.

Therefore, option E -
`(60^\circ, 45^\circ, 75^\circ)` set represent angle measures that could be found in a triangle.