1.

1. Find x if 6x and 3x are (a) Complementary angles (b) supplementary angles

Answer» <html><body><p><strong>Answer:</strong></p><p>a) 10°</p><p>b) 20°</p><p><strong>Step-by-step explanation:</strong></p><p></p><p>As per the provided information in the given question, we have :</p><p></p><ul><li>6x and 3x are complimentary angles. (Case 1)</li><li>6x and 3x are supplementary angles. (Case 2)</li></ul><p></p><p>We are asked to calculate the <strong>value</strong><strong> </strong><strong>of</strong><strong> </strong><strong>x</strong> in <strong>both</strong><strong> </strong><strong>cases</strong>.</p><p></p><p><img align="absmiddle" alt="\underline{ \bf{ \maltese \; \; \; Case \: 1 \: : \; \; \; }}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cbf%7B%20%5Cmaltese%20%5C%3B%20%5C%3B%20%5C%3B%20Case%20%5C%3A%201%20%5C%3A%20%20%20%3A%20%5C%3B%20%5C%3B%20%5C%3B%20%20%7D%7D%20" title="\underline{ \bf{ \maltese \; \; \; Case \: 1 \: : \; \; \; }}"/></p><p></p><p>If the <strong>sum of <a href="https://interviewquestions.tuteehub.com/tag/two-714195" style="font-weight:bold;" target="_blank" title="Click to know more about TWO">TWO</a> angles</strong> is <strong>90°</strong>, then they are <a href="https://interviewquestions.tuteehub.com/tag/called-907796" style="font-weight:bold;" target="_blank" title="Click to know more about CALLED">CALLED</a> complimentary angles to each other. Here, <strong>6</strong><strong>x</strong><strong> </strong>and <strong>3</strong><strong>x</strong> are two angles are complimentary angles, so their sum will be 90°.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { 6x + 3x = 90^\circ}} \\" class="latex-formula" id="TexFormula2" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%206x%20%2B%203x%20%3D%2090%5E%5Ccirc%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { 6x + 3x = 90^\circ}} \\"/></p><p></p><p>Performing addition of the <a href="https://interviewquestions.tuteehub.com/tag/terms-1242559" style="font-weight:bold;" target="_blank" title="Click to know more about TERMS">TERMS</a> in <a href="https://interviewquestions.tuteehub.com/tag/lhs-537115" style="font-weight:bold;" target="_blank" title="Click to know more about LHS">LHS</a>.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { 9x = 90^\circ}} \\" class="latex-formula" id="TexFormula3" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%209x%20%3D%2090%5E%5Ccirc%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { 9x = 90^\circ}} \\"/></p><p></p><p>Transposing 9 from LHS to <a href="https://interviewquestions.tuteehub.com/tag/rhs-614248" style="font-weight:bold;" target="_blank" title="Click to know more about RHS">RHS</a>, its arithmetic operator will get changed.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { x = \cancel{\dfrac{90^\circ}{9}} }} \\" class="latex-formula" id="TexFormula4" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%20x%20%3D%20%5Ccancel%7B%5Cdfrac%7B90%5E%5Ccirc%7D%7B9%7D%7D%20%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { x = \cancel{\dfrac{90^\circ}{9}} }} \\"/></p><p></p><p>Dividing 90° by 9.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \quad\underline{\boxed { \textbf{\textsf{ x = 10}}^\circ}} \\" class="latex-formula" id="TexFormula5" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Cquad%5Cunderline%7B%5Cboxed%20%7B%20%5Ctextbf%7B%5Ctextsf%7B%20x%20%3D%2010%7D%7D%5E%5Ccirc%7D%7D%20%5C%5C%20" title="\longrightarrow \quad\underline{\boxed { \textbf{\textsf{ x = 10}}^\circ}} \\"/></p><p></p><p>The value of x if <strong>6</strong><strong>x</strong> and <strong>3</strong><strong>x</strong><strong> </strong>are complimentary angles is <strong>1</strong><strong>0</strong><strong>°</strong>.</p><p></p><p><img align="absmiddle" alt="\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\" class="latex-formula" id="TexFormula6" src="https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cqquad%5Cqquad%5Cqquad%5Cqquad%5Cqquad%5Cqquad%5Cqquad%5Cqquad%7D%20%5C%5C%20" title="\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\"/></p><p></p><p><img align="absmiddle" alt="\underline{ \bf{ \maltese \; \; \; Case \: 2 \: : \; \; \; }}" class="latex-formula" id="TexFormula7" src="https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cbf%7B%20%5Cmaltese%20%5C%3B%20%5C%3B%20%5C%3B%20Case%20%5C%3A%202%20%5C%3A%20%20%20%3A%20%5C%3B%20%5C%3B%20%5C%3B%20%20%7D%7D%20" title="\underline{ \bf{ \maltese \; \; \; Case \: 2 \: : \; \; \; }}"/></p><p></p><p>If the sum of two angles is <strong>180°</strong>, then they are called supplementary angles to each other. Here, <strong>6x</strong> and <strong>3x</strong> are two angles are supplementary angles, so their sum will be <strong>180°</strong>.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { 6x + 3x = 180^\circ}} \\" class="latex-formula" id="TexFormula8" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%206x%20%2B%203x%20%3D%20180%5E%5Ccirc%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { 6x + 3x = 180^\circ}} \\"/></p><p></p><p>Performing addition of the terms in LHS.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { 9x = 180^\circ}} \\" class="latex-formula" id="TexFormula9" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%209x%20%3D%20180%5E%5Ccirc%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { 9x = 180^\circ}} \\"/></p><p></p><p>Transposing 9 from LHS to RHS, its arithmetic operator will get changed.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \sf{\quad { x = \cancel{\dfrac{180^\circ}{9}} }} \\" class="latex-formula" id="TexFormula10" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Csf%7B%5Cquad%20%7B%20x%20%3D%20%5Ccancel%7B%5Cdfrac%7B180%5E%5Ccirc%7D%7B9%7D%7D%20%7D%7D%20%5C%5C%20" title="\longrightarrow \sf{\quad { x = \cancel{\dfrac{180^\circ}{9}} }} \\"/></p><p></p><p>Dividing 180° by 9.</p><p></p><p><img align="absmiddle" alt="\longrightarrow \quad\underline{\boxed { \textbf{\textsf{ x = 20}}^\circ}} \\" class="latex-formula" id="TexFormula11" src="https://tex.z-dn.net/?f=%20%20%5Clongrightarrow%20%5Cquad%5Cunderline%7B%5Cboxed%20%7B%20%5Ctextbf%7B%5Ctextsf%7B%20x%20%3D%2020%7D%7D%5E%5Ccirc%7D%7D%20%5C%5C%20" title="\longrightarrow \quad\underline{\boxed { \textbf{\textsf{ x = 20}}^\circ}} \\"/></p><p></p><p>The value of x if <strong>6x</strong> and <strong>3x</strong> are supplementary angles is <strong>20°</strong>.</p></body></html>


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