Question

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

• A. ${35}^o$
• B. ${100}^o$
• C. ${110}^o$
• D. ${70}^o$

Answer 1

The correct option is D ${70}^o$

Given, the $△XYZ$ where $\angle YXZ={35}^o$

and $XY=YZ$. Therefore, $△XYZ$ 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) $\angle XYZ+\angle XYT={180}^o\Rightarrow \angle XYT={180}^o-\angle XYZ={180}^o-{110}^o={70}^o$

$\therefore \angle XYT={70}^o$.