Question

One of the acute angles of a right-angled triangle is 47º. Find the measure of the
other acute angle.
>​

Answer 1

Step-by-step explanation:

let the others acute angle be x

x + 47 + 90 = 180 ( asp)

x + 137 = 180

x = 180 - 137 = 43°

Answer 2

Answer : 43°

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Given :

• One angle = 47°
• Another angle = 90° ( as it is right angled triangle)
• Other angle = ?

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Solution:

• Let the 1st angle = 47°
• Let the 2nd angle = 90°
• Let the 3rd angle = x

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$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong> to </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>\:the\:</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong> Question :}} \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:</strong><strong> </strong><strong>x \: + \: 47 \: + \: 90 \: = \: 180</strong><strong> }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\ : \implies \displaystyle \sf \:</strong><strong>x \: + \: 137 \: = \: 180</strong><strong> \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\ : \implies \displaystyle \sf \:x \: = \: 180 </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>-</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>1</strong><strong>3</strong><strong>7</strong><strong> </strong><strong> \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: x \: </strong><strong>=</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>4</strong><strong>3</strong><strong>°</strong><strong> }} }\\ \\\end{gathered}\end{gathered}$

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Verfication:

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: x \: + \: 47 \: + \: 90 \: = \: 180 }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\ : \implies \displaystyle \sf \:</strong><strong>4</strong><strong>3</strong><strong> </strong><strong>\: + \: </strong><strong>4</strong><strong>7</strong><strong> </strong><strong>\:</strong><strong> </strong><strong>+</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>9</strong><strong>0</strong><strong> </strong><strong> = \: 180 \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: </strong><strong>1</strong><strong>8</strong><strong>0</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong> = \: 180 }} }\\ \\\end{gathered}\end{gathered}$

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Hence proved