Question

In a cyclic quadrilateral, the angles are (2x+7)°,(y+70 )°,(2y+7)°,(4x-5)°. Find measures of all angles

Answer 1

we know, in a cyclic quadrilateral opposite angles are supplementary
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$2x + 7 + 2y + 7 = 180 .....(1) \\ y + 70 + 4x - 5 = 180.....(2)$
Arranging ....(1)
$2x + 2y = 180 - 14 \\ > 2x + 2y = 166 \\ > x + y = 83........(3)$
Arranging ...(2)
$4x + y = 180 + 5 - 70 \\ > 4x + y = 115....(4)$
Subtracting ....(3) from...(4),
$4x + y - x - y = 115 - 83 \\ > 3x = 32 \\ > x = 32 \div 3 \\ > x = 10.6 \\ > y = 83 - 10.6 \\ > y = 72.4$
so x=10.6 and y=72.4