| The ratio between the adjacent angles of a parallelogram is 2: 3. Half the smaller angle of the parallelogram is equal to the smallest angle of a quadrilateral. Largest angle of quadrilateral is four times its smallest angle. |
| What is the sum of largest angle of quadrilateral and the smaller angle of parallelogram? |
A) \[252{}^\circ \]
B) \[226{}^\circ \]
C) \[144{}^\circ \]
D) \[180{}^\circ \]
E) None of these
Correct Answer: E
Solution :
| Let the adjacent angles of parallelogram be \[2x\]and \[3x,\]respectively. |
| Then, \[2x+3x=180{}^\circ \] |
| \[\Rightarrow \] \[5x=180{}^\circ \] |
| \[\Rightarrow \] \[x=36{}^\circ \] |
| \[\therefore \]Smaller angle, \[2x=72{}^\circ \] |
| \[\therefore \]Smallest angle of quadrilateral \[=36{}^\circ \] |
| \[\therefore \]Its largest angle \[=4\times 36{}^\circ =144{}^\circ \] |
| Hence, required sum \[=144{}^\circ +72{}^\circ =216{}^\circ \] |
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