Question 1

Hello! I need a little bit of help with this question please. (As of now this is not from an active test, this is a question from a book I am studying in order to take my Army ASVAB later.)

Hello! I need a little bit of help with this question please. (As of now this is not-example-1

Question 2

Solution:

Given a triangle;

Where

$\begin{gathered} RS=RT \\ m\operatorname{\angle}RTS=m\operatorname{\angle}RST\operatorname{\lparen}\text{base angle of an }\imaginaryI\text{sosceles tr}\imaginaryI\text{angle}\operatorname{\rparen} \end{gathered}$

To find the measure of angle S, i.e.

$\begin{gathered} m\angle RST \\ m\operatorname{\angle}RTS+m\operatorname{\angle}RST+m\angle SRT \end{gathered}$

Where

$\begin{gathered} m\operatorname{\angle}RTS=m\operatorname{\angle}RST\text{ be represented by x} \\ m\angle SRT=70\degree \end{gathered}$

Then,

$\begin{gathered} m\operatorname{\angle}RTS+m\operatorname{\angle}RST+m\angle SRT=180\degree\text{ \lparen Sum of angles in a triangle\rparen} \\ x+x+70\degree=180\degree \\ Collect\text{ like terms} \\ 2x=180\degree-70\degree \\ 2x=110\degree \\ x=(110\degree)/(2) \\ x=55\degree \end{gathered}$

Recall that;

$\begin{gathered} m\operatorname{\angle}RTS=m\operatorname{\angle}RST=x=55\degree \\ And; \\ Measure\text{ of angle S}=m\angle RST=55\degree \end{gathered}$

Hence, the measure of angle S is 55°

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