Mathematics

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


ANSWER

$$70^o$$


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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