Gujarat BoardEnglish MediumSTD 7MATHSProperties of Triangles2 Marks
Question
In a $\triangle\text{DEF}$, if $\angle\text{E} = 105^\circ$and $\angle\text{F} = 40^\circ$, find $\angle\text{D}$.
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Answer
In $\triangle\text{DEF}$, $\angle\text{E} = 105^\circ$, and $\angle\text{F} = 40^\circ$ But $\angle\text{D}+\angle\text{E}+\angle\text{F}=180^\circ$ (sum of angles of a triangle) $\Rightarrow\angle\text{D}+105^\circ+40^\circ=180^\circ$
$\Rightarrow\angle\text{D}+145^\circ=180^\circ$
$\Rightarrow\angle\text{D}=180^\circ-145^\circ$
$\Rightarrow\angle\text{D}=35^\circ$
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