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Question

Answers

(a) 35$^{\circ }$

(b) 100$^{\circ }$

(c) 110$^{\circ }$

(d) 70$^{\circ }$

Answer
Verified

We are given that in the below figure,

XY = YZ, and

$\angle YXZ$ = 35$^{\circ }$

If XY = YZ then $\Delta XYZ$ is an isosceles triangle and we know that,

In an isosceles triangle angles made by the equal sides with the other side of the triangle are equal, so

$\angle YXZ=\angle YZX$,

Hence we get

\[\angle YZX={{35}^{\circ }}\]

Now using the property of the triangles that sum of all three interior angles of a triangle is equal to 180$^{\circ }$, we get

$\angle YXZ+\angle YZX+\angle XYZ={{180}^{\circ }}$

Hence, we have

$\begin{align}

& {{35}^{\circ }}+{{35}^{\circ }}+\angle XYZ={{180}^{\circ }} \\

& \angle XYZ={{180}^{\circ }}-{{70}^{\circ }} \\

& \angle XYZ={{110}^{\circ }} \\

\end{align}$

Now, we know that sum of the linear pair of angles is 180$^{\circ }$, and we can observe that$\angle XYZ\,\,and\,\,\angle XYT$ are linear pair of angles hence,

\[\begin{align}

& \angle XYT+\angle XYZ={{180}^{\circ }} \\

& \angle XYT={{180}^{\circ }}-\angle XYZ \\

& \angle XYT={{180}^{\circ }}-{{110}^{\circ }} \\

& \angle XYT={{70}^{\circ }} \\

\end{align}\]

Hence, we got our answer as 70$^{\circ }$

Hence,

$\angle XYT=\angle YXZ+\angle YZX={{35}^{\circ }}+{{35}^{\circ }}={{70}^{\circ }}$

So, this is a very easy method through which we can solve our given problem.