Question

In the figure.$AB||CD$ , $\angle PTB={55}^{\circ }$ and $\angle DVS={45}^{\circ }$ sum of $\angle CUQ$ and $\angle RTP$ is -

• A. ${165}^{\circ }$
• B. ${155}^{\circ }$
• C. ${135}^{\circ }$
• D. ${105}^{\circ }$

Answer 1

Answer: (C)

The correct option is C ${135}^{\circ }$

Since, $AB||CD$, therefore,

$\angle BTV=\angle DVS={45}^{\circ }$ [Pair of Corresponding angles]

Also, $RS$ is s straight line and hence,

$\therefore \angle BTV+\angle PTB+\angle RTP={180}^{\circ }$ [Sum of angles on a line is ${180}^{\circ }$]

$\Rightarrow \angle RTP={180}^{\circ }-({45}^{\circ }+{55}^{\circ })$

$\Rightarrow \angle RTP={80}^{\circ }$...(i)

Also, $\angle RTA=\angle BTV={45}^{\circ }$ [Vertically opposite angles]

Hence, $\angle TUC=\angle RTA={45}^{\circ }$ [ [Pair of Corresponding angles]

Now, $\angle TUC+\angle CUQ={180}^{\circ }$ [Linear Pair]

$\Rightarrow \angle CUQ={180}^{\circ }-{45}^{\circ }={135}^{\circ }$...(ii)

From (i) and (ii)

$\angle CUQ+\angle RTP={80}^{\circ }+{135}^{\circ }={215}^{\circ }$