Question

Please help I request

Answer 1

Answer:

Now u can easily find the remaining values hope it helps

Answer 2

Given:-

$\red{➤}\:$$\sf m\angle R = (7+9x)⁰$

$\red{➤}\:$$\sf m\angle XTR = (7x+55)⁰$

$\red{➤}\:$$\sf m \angle TSR = (2x)⁰$

To Find:-

$\orange{☛}\:$$\sf x$

$\orange{☛}\:$$\sf m \angle XTR$

$\orange{☛}\:$$\sf m \angle RTS$

$\orange{☛}\:$$\sf m \angle R$

$\orange{☛}\:$$\sf m \angle S$

Solution:-

$\underline{\tt{Formula\:Applied}}$

In triangle-

$\green{ \underline { \boxed{ \sf{Sum\: of\: two\: opposite\:interior\:angle= Exterior \:Angle}}}}$

$\green{ \underline { \boxed{ \sf{Sum\:of\:all\:interior\:angle=180⁰}}}}$

$\underline{\tt\pink{Putting \:Values-}}$

$\sf Sum\: of\: two\: opposite\:interior\:angle= Exterior \:Angle$

$\begin{gathered}\\\quad\longrightarrow\quad \sf m\angle R+m\angle S = m\angle XTR \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf (7+9x)+(2x) = (7x+55)\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 7+9x+2x = 7x+55\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 11x+7= 7x+55\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 11x-7x= 55-7\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 4x= 48\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf x= \frac{48}{4}\\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \red{\boxed{\sf x= 12}}\\\end{gathered}$

Now putting values to find required angles-

$\sf m\angle R = (7+9x)⁰$

$\sf \qquad \:\:= (7+9\times12)⁰$

$\sf \qquad \:\:= (7+108)⁰$

$\sf \purple{\boxed{\sf m\angle R = 115⁰}}$

$\sf m\angle XTR = (7x+55)⁰$

$\sf \qquad \: \:\:= (7\times 12+55)⁰$

$\sf \qquad \: \:\:= (84+55)⁰$

$\sf \green{\boxed{m\angle XTR = 139⁰}}$

$\sf m\angle S= (2x)⁰$

$\sf \qquad \:\:= (2 \times 12)⁰$

$\sf \orange{\boxed{\sf m\angle S = 24⁰}}$

Also,

$\bf{\red{Sum\:of\:all\:interior \:angle \:of\:angle\:of\:triangle}=180⁰}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf m\angle S+m\angle R+m\angle RTS =180⁰ \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 24⁰+115⁰+m\angle RTS =180⁰ \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 139⁰+m\angle RTS =180⁰ \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf m\angle RTS =180⁰-139⁰ \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \red{\boxed{\sf m\angle RTS =41⁰}} \\\end{gathered}$