CTET old question paper problem on Pentagon скачать в хорошем качестве

CTET old question paper problem on Pentagon

:If a problem gives you a single interior angle, do not use the complex interior formula first. Instead:Step 1: Find the exterior angle: \(180^{\circ }-\text{Interior\ Angle}\).Step 2: Find the number of sides: \(n=\frac{360^{\circ }}{\text{Exterior\ Angle}}\).Example: If an interior angle is \(144^{\circ }\), the exterior is \(36^{\circ }\) (\(180-144\)). Thus, \(n=360/36=10\) (Decagon).Ratio Method (Common CTET Question):If the ratio of Interior to Exterior is given as \(x:y\), use this shortcut:\(\text{Number\ of\ Sides\ }(n)=\frac{2(x+y)}{y}\)Example: If the ratio is \(3:2\), then \(n=\frac{2(3+2)}{2}=5\).Quick Diagonals Formula:If you need the number of diagonals for a given \(n\):Formula: \(\frac{n(n-3)}{2}\). Summary of Important Polygon Values for CTET Polygon Name Sides (\(n\))Sum of Interior AnglesEach Int. Angle (Regular)Triangle3\(180^{\circ }\)\(60^{\circ }\)Quadrilateral4\(360^{\circ }\)\(90^{\circ }\)Pentagon5\(540^{\circ }\)\(108^{\circ }\)Hexagon6\(720^{\circ }\)\(120^{\circ }\)Octagon8\(1080^{\circ }\)\(135^{\circ }\)Decagon