<PRE><B>Question 982145</B>


Let &amp;nbsp;&lt;B&gt;x&lt;/B&gt;&amp;nbsp; be the measure of the angle &amp;nbsp;&lt;I&gt;L&lt;/I&gt;&lt;B&gt;D&lt;/B&gt;: &amp;nbsp;&amp;nbsp;x = m(&lt;I&gt;L&lt;/I&gt;&lt;B&gt;D&lt;/B&gt;)&amp;nbsp; (in degrees).


Then the measure of the angle &amp;nbsp;&lt;I&gt;L&lt;/I&gt;&lt;B&gt;E&lt;/B&gt;&amp;nbsp; be &amp;nbsp;3&lt;B&gt;x&lt;/B&gt;, &amp;nbsp;and the measure of the angle &amp;nbsp;&lt;I&gt;L&lt;/I&gt;&lt;B&gt;F&lt;/B&gt;&amp;nbsp; be &amp;nbsp;3&lt;B&gt;x&lt;/B&gt; - 9° &amp;nbsp;degrees.


Since the sum of interior angles of a triangle is equal to 180°, &amp;nbsp;you have an equation


x + 3x + (3x - 9) = 180.


Simplify and solve it:


7x - 9 = 180,


7x = 180 + 9,


7x = 189,


x = {{{189/7}}} = 27°.


Hence, &amp;nbsp;m(&lt;I&gt;L&lt;/I&gt;&lt;B&gt;D&lt;/B&gt;) = 27°, &amp;nbsp;m(&lt;I&gt;L&lt;/I&gt;&lt;B&gt;E&lt;/B&gt;) = 3*27° = 81°, and &amp;nbsp;m(&lt;I&gt;L&lt;/I&gt;&lt;B&gt;E&lt;/B&gt;) = 81° - 9° = 72°.


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