Question

In $△RST,m\angle R=90$and $m\angle s>20.$What can you say about $m\angle T$?

Short answer

In $\Delta RST,m\angle R=90$and $m\angle S>20$then $\mathit{m}\mathbf{\angle }\mathit{T}\mathbf{<}\mathbf{70}$.

Step-by-step solution

Step 1. Apply an angle sum theorem.

The sum of measures of all interior angles of a triangle is $180°$.

Step 2. Description of step.

In $\Delta RST$,

$m\angle R+m\angle S+m\angle T=180$

But for $m\angle S>20$,

$\begin{array}{c}m\angle R+m\angle S+m\angle T<180\\ 90+20+m\angle T<180\end{array}$

Step 3. Description of step.

Simplify the equation obtained in the step 2.

$\begin{array}{c}110+m\angle T<180\\ 110+m\angle T-110<180-110\\ m\angle T<70\end{array}$

Therefore, it can be said that $m\angle T$is less than 70.