Question

In the given figure(not drawn to scale), $\angle$UVT$={72}^o$ and $\angle$TSZ$={53}^o$, then find $\angle$XYZ.

• A. ${60}^o$
• B. ${125}^o$
• C. ${180}^o$
• D. None of these

Answer 1

The correct option is D None of these

Given in the figure

$UV||XZ$ both lines are parallel

$\Rightarrow \angle XZY=\angle UVT={72}^{\circ }$ corresponding angles of parallel are equal

$ST||XY$ both lines are parallel

$\Rightarrow \angle ZXY=\angle TSZ={53}^{\circ }$ corresponding angles of parallel are equal

In a $\Delta XYZ$

sum of all angles of a triangle $={180}^{\circ }$

$\Rightarrow \angle XYZ+\angle XZY+\angle ZXY={180}^{\circ }$

$\Rightarrow \angle XYZ+{72}^{\circ }+{53}^{\circ }={180}^{\circ }$

$\Rightarrow \angle XYZ+{125}^{\circ }={180}^{\circ }$

$\Rightarrow \angle XYZ={55}^{\circ }$

So, answer is None of these.