Question

In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.

m∠R > 90°
m∠S + m∠T < 90°
m∠S = m∠T
m∠R > m∠T
m∠R > m∠S
m∠S > m∠T

Answer 1

Answer:<R > 90°, <S + <R < 90°, <R > <T, <R > <S

Explanation:

Answer 2

∠ R
`>` 90°

`\angle s + \angle T < \angle 90`

`\angle R  > \angle T`

`\angle R  > \angle S`

Explanation:

Given that in triangle RST

`\angle R> (\angle s +\angle T)`

Now as per condition one angle is greater than sum of other two angles.

Since in triangle ,sum of all three angles = 180°

Hence if one angle is 90° then sum of other two must be equal to 90°

And if one angle is 90° then only other two angle be 45° each

Here Let if angle s = angle T = 30° then with this condition angle r is 120° , which is greater than 90°

So, from above it conclude that

For ,
`\angle R> (\angle s +\angle T)`

∵ ∠ R = 120° , then it is greater than 90°

I.e , ∠ R
`>` 90°

`\angle s + \angle T < \angle 90`

`\angle R  > \angle T`

`\angle R  > \angle S` Answer