In Quadrilateral = 38^ , = 3 , = 4 . Find the value of = ? - Vidyadip

MCQ

In Quadrilateral $\angle\text{A} = 38^\circ, \ \angle\text{C} = 3\angle\text{A},\ \angle\text{D} = 4\angle\text{A}.$ Find the value of $\angle\text{B}=\ ?$

A
57º
B
56º
C
55º
D
80º

✓

Answer

56º
Solution:
$\angle\text{A} + \angle\text{B} + \angle\text{C} + \angle\text{D} = 360^\circ$ (angle sum property)
$\angle\text{C} = 3 ( 38) = 114^\circ$
$\angle\text{D} = 4 ( 38) = 152^\circ$
So, $38^\circ + \angle\text{B} + 114^\circ + 152^\circ = 360^\circ$
$\angle\text{B} = 360^\circ - 304^\circ = 56^\circ$

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