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​

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

Answers ( )

    0
    2021-08-13T23:42:04+00:00

    Answer:

    AnswEr :

    ⠀⠀⠀⌬ 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.

    \begin{gathered}\twoheadrightarrow\sf M + N = 9 \qquad\quad\qquad\quad\Bigg\lgroup\sf eq^{n}\;(1)\Bigg\rgroup\\\\\end{gathered}

    ↠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

    \begin{gathered}\longrightarrow\sf N = 3 + M \qquad\quad\qquad\quad\Bigg\lgroup\sf eq^{n}\;(2)\Bigg\rgroup\\\\\end{gathered}

    ⟶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

    \begin{gathered}\twoheadrightarrow\underline{\boxed{\pmb{\sf{ Original\; Number =36}}}}\\\\\end{gathered}

    OriginalNumber=36

    OriginalNumber=36

    \;\;\;\;\;\qquad\therefore{\underline{\textsf{Hence, the Original number is \textbf{36}.}}}∴

    Hence, the Original number is 36.

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )