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