Mathematics

If the given figure ,if $XY$=$YZ$ then $\angle XYT=?$

$70^o$

SOLUTION
Given, the $\triangle XYZ$ where $\angle YXZ={ 35 }^{ o }$
and $XY=YZ$. Therefore, $\triangle XYZ$ is an isosceles triangle.
So, $\angle YXZ=\angle YZX={ 35 }^{ o }$ ( since, angles made by the equal sides with the other side of the triangle respectively.)
$\therefore \angle XYZ={ 180 }^{ o }-\angle YXZ-\angle YZX\\$
$={ 180 }^{ o }-{ 35 }^{ o }-{ 35 }^{ o }={ 180 }^{ o }-{ 70 }^{ o }={ 110 }^{ o }$
Now, $\angle XYZ+\angle XYT={ 180 }^{ o }\\$ ( since, they are supplementary angles) $\angle XYZ+\angle XYT={ 180 }^{ o }\\ \Rightarrow \angle XYT={ 180 }^{ o }-\angle XYZ={ 180 }^{ o }-{ 110 }^{ o }={ 70 }^{ o }$
$\therefore \angle XYT={ 70 }^{ o }$.

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Single Correct Medium Published on 09th 09, 2020
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