PP1 (Shorter) Quant Section 2 (Easy) Q8

<p><span style="color:#27ae60;"><span style="font-size:20px;">Solving the Problem</span></span></p> <p>This is another one of those <span style="color:#8e44ad;">Multiple-Select</span> problems in which we have to calculate the&nbsp;<strong>minimum</strong>&nbsp;possible value and the&nbsp;<strong>maximum</strong>&nbsp;possible value and also choose all values between those two.</p> <p><strong>Calculating the maximum possible value of&nbsp;$\angle F$:</strong></p> <p>We know that the three angles in a triangle sum to $180$ degrees. Thus, $\angle D + \angle E + \angle F = 180$. To find the maximum possible value of $\angle F$, let&#39;s assume that $\angle E = 90$. I know it must be greater than $90$ in reality, but we&#39;re making this assumption to find a boundary.</p> <p style="text-align: center;">$$25 + 90 + \angle F = 180$$</p> <p style="text-align: center;">$$\angle F = 180 - 25 - 90 = 65$$</p> <p>So we know that $\angle F &lt; 65$.</p> <p><strong>Calculating the minimum possible value of&nbsp;$\angle F$:</strong></p> <p>Let&#39;s assume that $\angle E$ is as large as possible to minimize $\angle F$. Let&#39;s assume that $\angle E = 155$. This is not possible in reality because it would mean that two angles alone in the triangle sum to $180$, but that&#39;s okay for our purposes. We&#39;re simply calculating a boundary.</p> <p style="text-align: center;">$$25 + 155 + \angle F = 180$$</p> <p style="text-align: center;">$$\angle F = 180 - 25 - 155 = 0$$</p> <p>So we know that $\angle F &gt; 0$.</p> <p><strong>Combining the maximum and minimum into one inequality:</strong></p> <p style="text-align: center;">$$0 &lt; \angle F &lt; 65$$</p> <p>Thus, <strong><span style="color:#27ae60;">the correct answers are A, B, C, and D</span></strong>.</p>