## In the figure 10.13, ZA = 75° and CE || AB. If ZECD = 40°, find the other twee of the triangle ABC. A 75° E 40°

Question

In the figure 10.13, ZA = 75° and CE || AB. If ZECD = 40°, find the other twee
of the triangle ABC.
A
75°
E
40°
B
С
D
Fig. 10.13​

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1 month 2021-08-13T23:40:08+00:00 1 Answer 0 views 0

⠀⠀⠀⌬ Let the Unit’s place digit = M

⠀⠀⠀⌬ And the ten’s place digit = N

⠀⠀⠀⌬ Then, Original Number = 10(M + N)

⠀⠀⠀⌬ Also, Interchaged Number = 10(N + M)

• F i r s t⠀C o n d i t i o n :

Sum of the two digits (M + N) number is 9.

↠M+N=9

eq

n

(1)

• S e c o n d⠀C o n d i t i o n :

After Interchanging the digits, the new number is greater than the original number by 27.

\begin{gathered}\longrightarrow\sf (10N + M) – (10M + N) = 27\\\\\\\end{gathered}

⟶(10N+M)−(10M+N)=27

\begin{gathered}\longrightarrow\sf 9N – 9M = 27\\\\\\\end{gathered}

⟶9N−9M=27

\begin{gathered}\longrightarrow\sf N – M = 3\\\\\\\end{gathered}

⟶N−M=3

⟶N=3+M

eq

n

(2)

\begin{gathered}\underline{\bigstar\:\sf{Substitue \: the \: value \: of \: N \: from \: eq^n \: (2) \: to \: eq^n \: (1) : }} \\ \\ \\ \end{gathered}

★SubstituethevalueofNfromeq

n

(2)toeq

n

(1):

\begin{gathered}\longrightarrow\sf M + N = 9\\\\\\\end{gathered}

⟶M+N=9

\begin{gathered}\longrightarrow\sf M + 3 + M = 9\\\\\\\end{gathered}

⟶M+3+M=9

\begin{gathered}\longrightarrow\sf 2M = 9 – 3 \\\\\\\end{gathered}

⟶2M=9−3

\begin{gathered}\longrightarrow\sf 2M = 6\\\\\\\end{gathered}

⟶2M=6

\begin{gathered}\longrightarrow\sf M = \cancel\dfrac{6}{2}\\\\\\\end{gathered}

⟶M=

2

6

\begin{gathered}\longrightarrow\sf M = 3\\\\\end{gathered}

⟶M=3

\begin{gathered}\underline{\bigstar\:\sf{Substituting\;value\;of\;M\;in\;\;eq^n\;(1)\;: }} \\ \\ \\ \end{gathered}

★SubstitutingvalueofMineq

n

(1):

\begin{gathered}\longrightarrow\sf M + N = 9\\\\\\\end{gathered}

⟶M+N=9

\begin{gathered}\longrightarrow\sf 3 + N = 9\\\\\\\end{gathered}

⟶3+N=9

\begin{gathered}\longrightarrow\sf N = 9 – 3\\\\\\\end{gathered}

⟶N=9−3

\begin{gathered}\longrightarrow\sf N = 6\\\\\end{gathered}

⟶N=6

\begin{gathered}\underline{\bigstar\:\textsf{Now,\;Original\; Number\; :}}\\\\\end{gathered}

★Now,OriginalNumber:

\begin{gathered}\twoheadrightarrow\sf Original\; Number = 10(M + N)\\\\\\\end{gathered}

↠OriginalNumber=10(M+N)

\begin{gathered}\twoheadrightarrow\sf Original\; Number = 10(3) + 6\\\\\\\end{gathered}

↠OriginalNumber=10(3)+6

\begin{gathered}\twoheadrightarrow\sf Original\; Number = 30 + 6\\\\\\\end{gathered}

↠OriginalNumber=30+6