Answer: [tex]\Large\boxed{\angle DAB=62^\circ}[/tex]
Concept:
Here, we need to know about the idea of a cyclic quadrilateral.
In a cyclic quadrilateral, the sum of either pair of opposite angles is supplementary, which means they add up to 180°.
Please refer to the attachment below for a graphical explanation
Solve:
Given information
∠DAB = 2x + 4
∠ABC = 4y + 4
∠BCD = 4x + 2
∠CDA = 3y + 8
Derived formula from the concept
∠DAB + ∠BCD = 180°
∠ABC + ∠CDA = 180° (Not Important)
Substitute values into the formula that includes ∠DAB
∠DAB + ∠BCD = 180°
(2x + 4) + (4x + 2) = 180
Combine like terms
2x + 4 + 4x + 2 = 180
2x + 4x + 4 + 2 = 180
6x + 6 = 180
Subtract 6 on both sides
6x + 6 - 6 = 180 - 6
6x = 174
Divide 6 on both sides
6x / 6 = 174 / 6
x = 29
Substitute values into the angle expression of ∠DAB
∠DAB = 2x + 4
∠DAB = 2 (29) + 4
∠DAB = 58 + 4
[tex]\Large\boxed{\angle DAB=62^\circ}[/tex]
Hope this helps!! :)
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