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Properties of Triangles — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsProperties of Triangles4 Marks
Question
AC, AD and AE are joined. Find.
$\angle \text{FAB}+\angle \text{ABC}+\angle \text{BCD}+\angle \text{CDE} +\angle \text{DEF}+\angle \text{EFA}$
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Answer


We know that sum of the angles of a triangle is 180°
Therefore in $\triangle \text{ABC},$ we have
$\angle \text{CAB}+\angle \text{ABC}+\angle \text{BCA}=180^\circ...(\text{i})$
In $\triangle \text{ACD},$ we have
$\angle \text{DAC}+\angle \text{ACD}+\angle \text{CDA}=180^\circ...(\text{ii})$
In $\triangle \text{ADE},$ we have
$\angle \text{EAD}+\angle \text{ADE}+\angle \text{DEA}=180^\circ...(\text{iii})$
In, $\triangle \text{AEF},$ we have
$\angle \text{FAE}+\angle \text{AEF}+\angle \text{EFA}=180^\circ...(\text{iv})$
Adding (i), (ii), (iii), (iv) we get
$\angle \text{CAB}+\angle \text{ABC}+\angle \text{BCA}+\angle \text{DAC}+\angle \text{ACD}\\+\angle \text{CDA}+\angle \text{AD}+\angle \text{ADE}+\angle \text{DEA}+\angle \text{FAE}\\+\angle \text{AEF}+\angle \text{EFA}=720^\circ$
Therefore $\angle \text{FAB}+\angle \text{ABC}+\angle \text{BCD}\\+\angle \text{CDE}+\angle \text{DEF}+\angle \text{EFA}=720^\circ$

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