MCQ
In quadrilateral $ABCD$, if $\angle\text{A} = 60^\circ$ and $\angle\text{B} : \angle\text{C} : \angle\text{D} = 2 : 3 : 7,$ then $\angle\text{D}$ is:
- ✓$175^{\circ}$
- B$180^{\circ}$
- C$25^{\circ}$
- D$50^{\circ}$
✓
Answer
Correct option: A.
$175^{\circ}$
In quadrilateral, the sum of the all four angles equal to 360º. let $\angle\text{B} = 2\text{x},\ \angle\text{C} = 3\text{x}$ and $\angle\text{D} = 7\text{x}.$
$\angle\text{A} + \angle\text{B} + \angle\text{C} +\angle\text{D} = 360^\circ$
$60 + 2x + 3x + 7x = 360$
$12x = 300^{\circ}$
$x = 25^{\circ}$
So, $\angle\text{D} = 7\text{x} = 7(25^\circ) = 175^\circ$
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