| In the given figure, XV is parallel to PQ. Find the value of the angles marked x and y. |
 |
A) \[27{}^\circ ,\]\[17{}^\circ \]
B) \[45{}^\circ ,\]\[25{}^\circ \]
C) \[70{}^\circ ,\]\[30{}^\circ \]
D) \[36{}^\circ ,\]\[16{}^\circ \]
Correct Answer: C
Solution :
| \[\angle EAY+\angle YAO+\angle OAB=180{}^\circ \][linear pair] |
| \[\Rightarrow \] \[60{}^\circ +40{}^\circ +\angle OAB=180{}^\circ \] |
| \[\Rightarrow \] \[\angle OAB=80{}^\circ \] |
| \[XY||PQ\]and AB is the transversal. |
| \[\angle EAY=\angle ABQ\][corresponding angles] |
| \[\Rightarrow \] \[\angle EAY=\angle ABO+\angle OBQ\] |
| \[\Rightarrow \] \[60{}^\circ =30{}^\circ +y\] |
| \[\Rightarrow \] \[y=30{}^\circ \] |
| In \[\Delta AOB,\]\[\angle AOB+\angle OBA+\angle BAO=180{}^\circ \] |
| \[x+30{}^\circ +80{}^\circ =180{}^\circ \] |
| \[\Rightarrow \] \[x=70{}^\circ \] |
| \[\Rightarrow \] \[x=70{}^\circ \] and \[y=30{}^\circ \] |
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